Tutors Answer Your Questions about Geometry Word Problems (FREE)
Question 570796: a rancher has 180 ft of fencing to enclose two adjacent rectangular corrals. A river forms one side of the corrals. Suppose the width of each corral is x ft. Express the total area of the two corrals as a function of x. Find the domain of the function.
Answer by ankor@dixie-net.com(12681)   (Show Source):
You can put this solution on YOUR website!a rancher has 180 ft of fencing to enclose two adjacent rectangular corrals.
A river forms one side of the corrals. Suppose the width of each corral is x ft.
Express the total area of the two corrals as a function of x. Find the domain of the function.
:
That would be 3 widths and 1 length, therefore
L + 3x = 180
L = (180-3x)
:
A = L * X
replace L with (180-3x)
A = x(180-3x)
A = -3x^2 + 180x; total area as a function of x
:
Graph y - -3x^2+180x
You can see max area when x=30 ft and domain is 0 to 60
Question 570937: the perimeter of a rectangle is 110 ft. and the area is 684 sq. ft. What is the length of the longer side
Answer by JBarnum(1826)  (Show Source):
Question 570897: to fence a rectangular farm of 750 m^2, 110 m of fence has been used. calculate the dimensions of the farm. show your work.
Answer by maa.veera@gmail.com(3) (Show Source):
You can put this solution on YOUR website!Area of rectangle = L * W = 750 m^2 -----(1)
Perimeter = 2(L + W )
110 = 2(L + W)
55 = L + W
W = 55 - L ------(2)
plug (2) in (1)
L(55 - L) = 750
55L - L^2 = 750
L^2 - 55L + 750 =0
(L -30)(L-25)=0
L = 30 or L =25
if L = 3 0 W = 55-30 = 25
if L=25 then W = 55-25 = 30
therefore dimensions of Rectangle are 30m and 25m .
Question 570724: The town of Foxton lies 10 mi north of an abandoned east-west road that runs through Grimley, as shown in the figure. The point on the abandoned road closest to Foxton is 60 mi from Grimley. County officials are about to build a new road connecting the two towns. They have determined that restoring the old road would cost $100,000 per mile, while building a new road would cost $200,000 per mile. How much of the abandoned road should be used (as indicated in the figure) if the officials intend to spend exactly $8.8 million?
How much would it cost to build a new road connecting the towns directly? (Round your answer to one decimal place.)
Answer by ankor@dixie-net.com(12681) (Show Source):
You can put this solution on YOUR website!The town of Foxton lies 10 mi north of an abandoned east-west road that runs through Grimley, as shown in the figure.
The point on the abandoned road closest to Foxton is 60 mi from Grimley.
County officials are about to build a new road connecting the two towns.
They have determined that restoring the old road would cost $100,000 per mile, while building a new road would cost $200,000 per mile.
How much of the abandoned road should be used (as indicated in the figure) if the officials intend to spend exactly $8.8 million?
:
This is a triangle problem has a right angle at a point on the old road directly south of Fox
:
Leg 1 = 10 mi
leg 2 = x, the distance from a point due south of F, to where the new road joins the old road
hypotenuse = new road distance
(60-x) = restored road distance
then
Road dist from F to G = hypotenuse + (60-x)
:
Cost: hypotenuse 200,000 per mile; (60-x) $100,000 per mile
:
Do this in 100 thousands of dollars, to avoid writing all these zeros
:
New road cost + old road cost = 8.8 million
 + 1(60-x) = 88
 = 88 - (60-x)
= 88 - 60 + x
= x + 28
Square both sides
4(100+x^2) = (x+28)^2
400 + 4x^2 = x^2 + 56x + 784
Combine like terms on the left
4x^2 - x^2 - 56x + 400 - 784 = 0
3x^2 - 56x - 384 = 0
we can use the quadratic formula here, but this will factor to:
(x-24)(3x+16) = 0
The positive solution
x = 24
then
New road construction dist:
 = 26 mi
:
Old road restored dist:
60 - 24 = 36 mi
:
If we did this right, the cost should be 8.8 million
26(200000) = $5,200,000
36(100000) = $3,600,000
------------------------
total road: $8,800,000 which is 8.8 million
:
:
How much would it cost to build a new road connecting the towns directly?
(Round your answer to one decimal place.)
That would be the hypotenuse again, only this time:
Cost =  = $12,165,525
:
How about this? Did all this make sense to you?
Question 570786: The perimeter of a rectangle is 2012, and lengths of all sides are integers. What is the smallest possible area of this rectangle?
Answer by KMST(576)  (Show Source):
You can put this solution on YOUR website!If  and  are the dimensions of this rectangle, we know that
 so   and 
The area, as a function of x is
That quadratic equation represents a parabola.
Its axis of symmetry is  
The maximum area occurs at , when the rectangle is a square.
Moving away from that point, to either side of , the area decreases.
Since the length of the sides are integers, the minimum will be for  and  , when one side measures 1 and the other 1005. It is the same solutionm no matter what side length we call x.
The minimum area is 1005.
Question 570613: this is a problem that my teacher gave me and no matter how I look at it it doesn't make any sense
The perimeter of an equilateral triangle is 9 inches more than the perimeter of a square, and the side of the triangle is 6 inches longer than the side of the square. Find the side of the triangle. (Hint: An equilateral triangle has three sides the same length.)
Answer by scott8148(5879)  (Show Source):
You can put this solution on YOUR website!"the side of the triangle is 6 inches longer than the side of the square" ___ t = s + 6 ___ t - 6 = s
"The perimeter of an equilateral triangle is 9 inches more than the perimeter of a square"
___ 3t = 4s + 9
substituting ___ 3t = 4(t - 6) + 9 ___ 3t = 4t - 24 + 9
Question 570089: I am having issues with this one problem in my home work. I don't know why I cant get it...We have to set it up in the 5 step and I guess I am just confused.
?. The perimeter of a rectangle is 36m. The length is 2m more than three thimes the width. Find the length and with of the rectangle.
Ok, so here is what I have done.
Data: I drew a rectangle with the length labeled as 3w + 2, and the width is just labeled as w.
Varaibles: P=2(3w+2)x 2w
Plan: P=2Lx2W
Equation: 36=2(3w+2)x 2w
Ok...so here is where I get stuck.
36=2(3w+2) x 2w
36=6w+4 x 2w
so I think now I subtract 4 from each side, but then I am stuck. Am I even close?
Answer by ankor@dixie-net.com(12681) (Show Source):
You can put this solution on YOUR website!I think you have the right idea, let's do it this way
Write an equation for each statement:
:
"The perimeter of a rectangle is 36m."
2L + 2W = 36
:
"The length is 2m more than three times the width."
L = 3W + 2
:
Replace L in the 2st equation with (3W+2); resulting in
2(3W+2) + 2W = 36
6W + 4 + 2W = 36: this is essentially what you did, just combine like terms, find W
8W = 36 - 4
8W = 32
W = 32/8
W = 4 m is the width
the
L = 3(4) + 2
L = 14 m is the length
;
:
Check our solutions by finding the perimeter with these values
2(14) + 2(4) =
28 + 8 = 36
Question 570159: In the rectangle below,AC has a length of 28. What is the length of ED If necessary, round your answer to two decimal places.
Answer by AnlytcPhil(1116)  (Show Source):
You can put this solution on YOUR website!
The diagonals of a rectangle have equal lengths. Since AC has a length of 28,
and AC is a diagonal, the other diagonal BD also has a length of 28.
The diagonals of a rectangle also bisect each other. So diagonal BD is
bisected by the other diagonal AC at point E. And since diagonal BD has
a length of 28 then BE and ED both have a length which is  of 28,
or 14 each.
Answer: ED has a length of 14.
Edwin
Question 570059: If your shadow is twice your height what is the angle of elevation of the sun
Answer by stanbon(48502) (Show Source):
You can put this solution on YOUR website!If your shadow is twice your height what is the angle of elevation of the sun
Draw the picture.
You have a right triangle with base = 2h ; height = h
----
The angle of elevation is opposite "h":
tan(e) = h/(2h)
tan(e) = 1/2
----
e = tan^-1(1/2) = 26.57 degrees
=================================
cheers,
Stan H.
================
Question 569492: A flower bed measuring 8 feet by 10 feet is bordered by a concrete walk that is 2 feet wide. What is the are of the concrete walk?
Answer by nerdybill(5403)  (Show Source):
You can put this solution on YOUR website!A flower bed measuring 8 feet by 10 feet is bordered by a concrete walk that is 2 feet wide. What is the are of the concrete walk?
.
area of flower bed: 8*10 = 80 sq ft
area of flower bed and walk: (8+4)(10+4)=12*14=168 sq ft
area of walk = "area of flower bed and walk" - "area of flower bed"
area of walk = 168 - 80 = 88 sq ft
Question 569387: Is m+n an integer, why or why not?
Answer by richard1234(4789)  (Show Source):
You can put this solution on YOUR website!What are m and n? If m and n are integers, then m+n is an integer. If m and n are not necessarily integers, m+n could be an integer (if and only if the fractional part of m plus the fractional part of n equals an integer, e.g. 3.7 + 1.3).
Question 569345: A record radius of 15cm. The label has a radius of 6cm. Find the following to the nearest tenth:
A. The area of the record (including the label).
B. The area of the label.
C. The area of the record that is not covered by the label.
Answer by solver91311(12117)  (Show Source):
You can put this solution on YOUR website!
The area of a circle is given by
The entire record is a circle of radius 15 cm. The label is a circle of radius 6 cm. The area of the record not covered by the label is the area of the entire record minus the area of the label.
John
My calculator said it, I believe it, that settles it
Question 569092: in a regular 31 gon what is the measurement of each interior angle and measurement of each exterior angle
Answer by KMST(576) (Show Source):
You can put this solution on YOUR website!The exterior angle is the angle between the line extending one side and the next side. In other words, it is the angle by which you change direction as you turn a corner (vertex) as make your way around the polygon, along the perimeter. Of course, the sum of all those angles shows how much you turned yourself around on one full lap along the perimeter: 360 degrees. If the polygon was a regular 31-gon, all 31 angles were the same so the measurement of each, in degrees is
The interior angle is the angle between consecutive sides inside the polygon. It is supplementary to the exterior angle, so its measurement, in degrees, is
However, maybe your teacher expected you to memorize and use some formula in the textbook that says that the sum of the interior angles of an n-gon is
The result is the same.
Question 569287: a right triangle has a perimeter of 1400. The hypotenuse is 600. What are the lengths of the other two sides?
Answer by lwsshak3(2907) (Show Source):
You can put this solution on YOUR website!a right triangle has a perimeter of 1400. The hypotenuse is 600. What are the lengths of the other two sides?
**
let x=length of one of the legs
1400-600-x=800-x=length of other leg
By Pythagorean Theorem:
600^2=x^2+(800-x)^2
360000=x^2+640000-1600x+x^2
2x^2-1600x+280000=0
x^2-800x+140000=0
solve by quadratic formula:
a=1, b=-800, c=140000
x=541.421
or
x=258.579
ans:
longer leg=541.421
other leg= 258.579
Question 568989: if the area of a trapazoid was 72 ft^2 and the sum of the bases was 48 ft what would the heighth be?
Answer by Theo(2967)  (Show Source):
You can put this solution on YOUR website!the formula for the area of a trapezoid is 1/2 times the sum of the bases times the height.
here's a reference for that.
http://www.mathgoodies.com/lessons/vol1/area_trapezoid.html
you are given that the area is 72 square feet and you are given that the sum of the bases if 48 feet.
plug that in the formula and you get:
formula is:
area = 1/2 * height * sum of bases
this becomes:
72 = 1/2 * height * 48 which becomes:
72 = 24 * height
divide both sides of this equation by 24 to get:
72/24 = height
this makes height equal to 3 feet.
the bases could be any length as long as their sum is equal to 48.
Question 568677: the length of a rectangular frame is 9 cm more than the width. the area inside the frame is 90 square cm. find the width of the frame. set up a quadratic equation to solve it. THANKS in advance
Answer by KMST(576) (Show Source):
You can put this solution on YOUR website!Let the width be cm.
The length (in cm) is  .
The area of the rectangle is length time width. In square centimeters, it's
If that is 90 square centimeters,
The expected quadratic equation answer is probably  , although and  are equivalent equations.
To solve it, you could factor, complete the square, or use the quadratic formula.
Factoring, we see that  so the equation transforms into
 with solutions  and  .
Since the width of a frame is measured as a positive number, the only solution to the problem is
 .
The width of the frame is 6 cm. The length is 15 cm (  ).
Question 568684: a regular-size piece of paper is about 28 centimeters from top to bottom. what is the length in milimeters?
Answer by Alan3354(21550)  (Show Source):
Question 568332: A rectangular swimming pool is surrounded by a concrete walkway of uniform width. The outside dimensions of the walkway is 13 ft. by 18 ft. The water surface of the pool is 50 ft(squared). What is the dimension of the pool?
Answer by KMST(576) (Show Source):
You can put this solution on YOUR website!WHAT WE KNOW
The product of length and width of the pool is the water surface of the pool and is 50 square feet.
The length (in feet) of the pool plus two widths of walkway is 18. That is 5 feet more than the width (in feet) of the pool plus two widths of walkway (13 feet). That means that the length of the pool itself is 5 feet longer than the width of the pool.
THE EASIER WAY TO THE SOLUTION
Assuming there is only one solution, all you have to do is find two numbers (for the length and width measurements of the pool, in feet) whose product is 50, and whose difference is 5.
I would say that 5 and 10 make a solution. The pool is 5 foot long and 10 foot wide. Two width of the surrounding walkway must be
8 ft = 13 ft - 5 ft = 18 ft - 10 ft,
so the walkway must be 4 ft wide.
THE FANCIER WAY (that I would use only if they make me)
If you have to prove that is the only solution and show off your algebra knowledge say that twice the width of the walkway (in feet) is , and that, as a consequence the with and length of the pool (in feet) must be  , and 
That would make the water surface area (in square feet)
 -->  --> 
Then solve the equation any which way you can to get the solutions  and  . You discard , because you cannot fit two 11.5 feet wide that both together add up to 23 feet plus a pool in a space that is 13 feet by 18 feet. So your only answer is 4 foot wide walkways and a pool with dimesnion (in feet) of
 , and 
Question 567874: A square lawn is surrounded by a path 2.5 m wide around it . If the area of the path is 200 sq m , find the area of the lawn
Answer by mananth(10539)  (Show Source):
You can put this solution on YOUR website!let the side be x
Area of square = side ^2
area = x^2
width = 2.5
length increases by 5 m
Area including width = (x+5)(x+5)= (x+5)^2
(x+5)^2-x^2=2000
x^2+10x+25-x^2=200
10x=200-25
10x=175
/10
x= 17.5 m
Question 567860: The length of a rectangle is 3 feet less than twice the width of the rectangle. If the perimeter of the rectangle is 84 feet, find the width and the length.
Width = _____ft
Length=______ft.
x+x+x+x=84
L=2w-3 is what i have come up with but i am not sure where to go from there.
Answer by rapaljer(4551)  (Show Source):
You can put this solution on YOUR website!Let x = width
2x-3= length
2W + 2L = Perimeter
2(x) + 2(2x-3) = 84
2x+4x-6=84
6x-6=84
6x-6=84+6
6x=90
x=15 ft Width
2x-3 = 2*15-3 = 27 ft Length
Check: 2*15 + 2*27
30 +54
84 It checks!!
For a complete explanation of this and other topics in WORD PROBLEmS, please see my own website. The best way to find it is to use the easy-to-remember and easy-to-spell link www.mathinlivingcolor.com. At the bottom of the page there is a single link that takes you to my Homepage. On my Homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time." Choose "Basic Algebra", and look in "Chapter 1" for "Sections 1.09 and 1.10." Here you will find my own non-traditional explanation that my own students used to find much easier to understand than most of the other textbooks being used. I also have lots of examples, exercises, and answers. In addition, most of the hardest problems are solved in color on the MATH IN LIVING COLOR pages that go with this topic. It's ALL FREE on my website!!!
To contact me please use my Email address at rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus
Question 567760: using proportional relationships. the scale is 1.5in:60ft
find the length of segment AB.segment AB equals .5in.
how do i solve for this because i guessed that 1in was half of 60 (30ft) & .5in might be half of 30 (15ft)? was i correct?
Answer by Alan3354(21550) (Show Source):
You can put this solution on YOUR website!using proportional relationships. the scale is 1.5in:60ft
find the length of segment AB.segment AB equals .5in.
how do i solve for this because i guessed that 1in was half of 60 (30ft) & .5in might be half of 30 (15ft)? was i correct?
-----------------
1.5 in = 60 ft
1 in = 40 ft
-----------------
0.5 in --> 20 ft
====================
or, 0.5 in is 1/3 of 1.5 in
60*(1/3) = 20 ft
Question 567625: A scuba diver has a taut rope connecting the dive boat to an anchor on the ocean floor. The rope is 110 ft long. The water is 55 ft deep. To the nearest tenth of a foot, how far is the anchor from a point directly below the boat?
--Basically, I need to know where each length goes. I used 55 as the height of the right triangle and 110 as the base. Is this correct?
Thank you.
Answer by Earlsdon(6098) (Show Source):
You can put this solution on YOUR website!Er...not quite!
The taut 110-foot rope connecting the anchor to the boat would be the hypotenuse of such a right triangle, but you're correct in using 55ft. as its height.
Now you need to apply the Pythagorean theorem to find the third side of this triangle (the base) which would give you the horizontal distance of the boat from the anchor.
 You need to find b (for base) to get your answer.
 Substitute  and 
 Take the square root of both sides.
 Round to the nearest tenth.
 feet.
Question 567609: The surface areas of two similar cylinders are 6ft2 and 54ft2. The volume of the smaller cylinder is 2ft3. What is the volume in cubic feet of the larger cylinder?
Answer by Alan3354(21550) (Show Source):
You can put this solution on YOUR website!The surface areas of two similar cylinders are 6ft2 and 54ft2. The volume of the smaller cylinder is 2ft3. What is the volume in cubic feet of the larger cylinder?
----------------
The surface areas of two similar cylinders are 6ft2 and 54ft2
The ratio of dimensions is 3 to 1.
------
The volume of the smaller cylinder is 2ft3. What is the volume in cubic feet of the larger cylinder?
----------
The ratio of the volumes is the cube of 3 to 1 = 27 to 1
--> 54 cubic ft
Question 567601: Solve
1/(1-x) = 3/(1+x)
Answer by htmentor(580)  (Show Source):
Question 567096: suppose the ratio of the volumes of two balls is 8 to 1. What is the ratio of their radii?
Answer by richard1234(4789) (Show Source):
You can put this solution on YOUR website!Volume is a function of r^3 (r is radius), and changing the unit length by a constant k will change the volume by a factor of k^3. Here, 8:1 = (2^3):(1^3) so the ratio of the radii must be 2:1.
Question 567303: the length of a rectangle is 6cm and the width 3 cm. if both are increased by the same amount the area is increased by 70 cm^2 find the length and width of the larger rectangle?
Answer by Horlaye(3)  (Show Source):
You can put this solution on YOUR website!Let the number increased be represented by x. Area of a rectangle = l * w. Therefore : l = 6 + x, w = 3 + x. Hence ( 6 + x ) ( 3 + x ) = 70, then we will expand.
18 + 6x + 3x + x^2 = 70 then,we
change it to quadratic equation
x^2+9x+18-70=0
x^2+9x-52=0
x^2-4x+13x-52=0
x(x-4)13(x-4)=0
(x+13)(x-4)=0
x+13=0 or x-4=0
x = -13 or x = 4
since the length can't take the negative. Therefore the increased number = 4 and the larger rectangle's length is 10cm and the width is 7cm.
Question 273868: Two poles, 30 feet and 50 feet tall, are 40 feet apart and perpendicular to the ground. The poles are supported by wires attached from the top of each pole to the bottom of the other, as in the figure. A coupling is placed at C where the tow wires cross.
Find x, the distance from C to the taller pole?
How high above the ground is the coupling?
How far down the wire from the smaller pole is the coupling?
Answer by noelsanoj(1) (Show Source):
You can put this solution on YOUR website!Let A be the distance from the ground to the coupling C (perpendicular to the ground and parallel to both poles)
Let D be the distance from the tallest poll to the point on the ground from C.
(Angle-Angle (AA) Similarity) two pair of similar triangles are formed.
Using proportions on the smaller pair of triangles to find the distance on the ground from under C to the largest pole.
30d = 40a
for the larger pair of triangles
50(40-d) = 40a
Notice 40a, substituting on both equations
30d)=50(40-d)
30a = 2000-50d
80d = 2000
d = 25 feet. If you subtract from 40 you get the other base which is 15ft.
Substitute to find the height of the coupling
30d = 40a
30(25)=40a
a=750/40
a=18.75 feet height.
How far down the wire from the smaller pole is the coupling?
Notice that the smaller pole formed a dilation by a factor 10 from a 3,4,5 triangle. Therefore, the wire from the smaller pole to the base of the larger is 50ft. Then using the Triangle Proportionality Theorem, formulate the following proportion.
Let y be the distance of the segment from the pole to C (Coupling) use the proportion.
y=18.75 feet
For the distance from C to the Taller pole, using Pythagoras
 the hypotenuse is about 64 feet round to the unit.
To find the distance from C to the taller pole, again use the Triangle Proportionality Theorem..
Let p be the distance from C to the Taller pole.
The distance is 40 feet.
Question 566994: The page of a book measures 6in by 9in. A uniform border around the page leaves 28in^2 for type. What are the dimensions of the type area?
I have no idea where to begin with this. How do I solve this?
Answer by stanbon(48502) (Show Source):
You can put this solution on YOUR website!The page of a book measures 6in by 9in. A uniform border around the page leaves 28in^2 for type. What are the dimensions of the type area?
-------------------------
Draw the picture of a rectangle inside a rectangle.
The outer rectangle (including the inner triangle)
has area = 6*9 = 54 sq in.
-------
The dimensions of the inner rectangle are:
width = 6-2x
length = 9-2x
------
Equation:
(6-2x)(9-2x) = 28
54 - 12x -18x + 4x^2 = 28
---
4x^2 - 30x + 26 = 0
---
2x^2 - 15x + 13 = 0
2x^2 - 13x - 2x + 13 = 0
x(2x-13)-(2x-13) = 0
(2x-13)(x-1) = 0
-------
Possible solutions:
x = 13/2 or x = 1
------
Find Width and length:
width = 6-2x
length = 9-2x
---
If x = 1 you get:
width = 6-2x = 4
length = 9-2x = 7
=========================
If x = (13/2) you get:
width = 6-2(13/2) is negative
length = 9-2(13/2) is negative
-----
So the only solution is width = 4 and length 7
===================================================
cheers,
Stan H.
=============
Question 566959: The length of a triangle is 4 m more than twice the length of the base. The area of the triangle is 35 m^2. Find the height of the triangle.
This is what I've done:
A=1/2*b*h
35= (1/2)*(2b)*(2b+4)
Is that the right equation? How do I solve this?
Answer by solver91311(12117) (Show Source):
Question 566833: Why does cos(85 degrees)+cos(95 degrees)= 0?
Answer by solver91311(12117) (Show Source):
Question 566801: if the perimetare of a rectangle is 30 then whats the area
Answer by Alan3354(21550) (Show Source):
You can put this solution on YOUR website!if the perimetare of a rectangle is 30 then whats the area
-------------
I assume you mean perimeter.
-----------
Not enough data.
It could be 1 by 14 = 14 sq units
2 by 13 = 26
3 by 12 = 36
pi by 15-pi = 15pi - pi^2
or an infinite # of other combinations.
Question 566592: a square garden has perimeter 96m find its side
Answer by rfer(10417) (Show Source):
Question 566544: a circle whose diameter has endpoints (-3,0) and (3,0)
Answer by stanbon(48502) (Show Source):
You can put this solution on YOUR website! a circle whose diameter has endpoints (-3,0) and (3,0)
--------
Center at the midpoint: (0,0)
---
radius = 3
---------
Equation:
x^2 + y^2 = 9
========================
Cheers,
Stan H.
Question 566272: A rectangular field is 30 feet wide and 50 feet long. Fence post are to be placed every 10 feet around the field. How many posts are needed?
Answer by ad_alta(170)  (Show Source):
You can put this solution on YOUR website!Place one in each of the four corners. Then you will need two more on each of the 30 ft sides. Also, you will need four more on each of the 50 ft sides. That gives 16 posts total.
Question 566203: the perimeter of a rectangle is 44 inches.Find the dimension if the width is two inches longer than three times the length.Then find the area of the rectangle
Answer by lwsshak3(2907) (Show Source):
You can put this solution on YOUR website!the perimeter of a rectangle is 44 inches.Find the dimension if the width is two inches longer than three times the length.Then find the area of the rectangle.
**
let x=length of rectangle
3x+2=width of rectangle
Perimeter=2*(length+width)=44
=2(x+3x+2)=2(4x+2)=8x+4=44
8x=40
x=5 (length
3x+2=17 (width)
Area of rectangle=length*width=5*17=85 sq in
Question 566135: I have a word problem on a sheet that I don't really understand. I would really love to know the steps to solving it since there are more of them. I've tried the pythagorean theorem, but I don't think I'm doing it right. I would greatly appreciate any help I receive.
In a square, the length of a side is 6 cm less than a diagonal. How long is each diagonal?
Answer by ankor@dixie-net.com(12681) (Show Source):
You can put this solution on YOUR website!In a square, the length of a side is 6 cm less than a diagonal.
How long is each diagonal?
:
Let c = the diagonal
then
a = the side of the square
then
c = (a+6)
:
Using pythag: a^2 + b^2 = c^2, (you're right about that!)
It's a square so a = b, so we can write it
2a^2 = (a+6)^2
FOIL (a+6)(a+6)
2a^2 = a^2 + 6a + 6a + 36
2a^2 = a^2 + 12a + 36
Combine like terms on the left
2a^2 - a^2 - 12a - 36 = 0
a^2 - 12a - 36 = 0
Use the quadratic formula
in this equation, x=a; a=1, b=-12, c=-36
:
:
we only want the positive solution here
a = 
a = 14.5 cm is the length of the side
but they want the diagonal
14.5 + 6 = 20.5 cm is the length of the diagonal
;
:
Check this on your calc: enter  results: 20.5
Question 566090: A polygon has five interior angles. It has two angles measuring 160° each, two angles measuring 75° each, and one angle measuring 70°. What kind of polygon is this?
Answer by Alan3354(21550) (Show Source):
You can put this solution on YOUR website!A polygon has five interior angles. It has two angles measuring 160° each, two angles measuring 75° each, and one angle measuring 70°. What kind of polygon is this?
----------
It has 5 angles --> pentagon
Question 566066: What is the formula to find the AREA between TWO Rectangles?
Answer by Alan3354(21550) (Show Source):
You can put this solution on YOUR website!What is the formula to find the AREA between TWO Rectangles?
---------
What does that mean?
One rectangle can be in Texas, and the other in Florida.
How can you find the area "between" them?
Question 566002: The ratio of the length and breadth of a rectangular farm is 2:1 . If its area is 450 m^2, find its length.
Answer by ad_alta(170) (Show Source):
You can put this solution on YOUR website!Let 'l' be the length and 'w' the width. Then l/w=2 and lw=450. Substituting w=l/2 into the second equation, we get l(l/2)=450. Therefore l=30.
Question 566016: the area of a rectangular vegetable plot is 15 square metres.if the width is 1 metre,what is its lenght?
Answer by ad_alta(170) (Show Source):
You can put this solution on YOUR website!Remember that the area of a rectangle is length times width. If the area in 15 square meters and one side in only one meter, the other side must be 15/1=15 meters long.
Question 565950: what is the perimeter of a square that measures 10 inches by 11 inches
Answer by mananth(10539) (Show Source):
Question 565866: Mr. Diaz measured the length of the garden. It measured 9 meters long. How many centimeters long was the garden?
Answer by solver91311(12117) (Show Source):
Question 565561: an above-ground swimming pool is in the shape of a regular hexagonal prism. the pool is 3 meters high and holds 66 cubic meters of water. another pool has a base with the same shape and size, but is 5 meters high. how much water will this pool hold? explain
Answer by ankor@dixie-net.com(12681) (Show Source):
You can put this solution on YOUR website!an above-ground swimming pool is in the shape of a regular hexagonal prism.
the pool is 3 meters high and holds 66 cubic meters of water.
another pool has a base with the same shape and size, but is 5 meters high.
how much water will this pool hold? explain
:
There is a direct relationship between the height and the volume
 = 
Cross multiply
3v = 5*66
v = 
v = 110 cu meters of water
| 
