# Questions on Word Problems: Geometry answered by real tutors!

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Question 994825: line segment AB has the endpoints A(-4,5) and B(3,5). what is the x-coordinate of a point C such that B is the midpoint of line segment AC
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given:
A(-4,5) and B(3,5)
The y-coordinates are both
That means this is a horizontal line
-----------------------------
C( x,5 ) are coordinates of point C
If B is the midpoint, I can say:

Point C is C( 10, 5 )

Question 994512:

Question 994400: I need to find the surface area of a 11 by 8 piece of paper when rolled into a cylinder.
Found 2 solutions by Alan3354, Cromlix:
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I need to find the surface area of a 11 by 8 piece of paper when rolled into a cylinder.
------------
11*8 = 88 sq units (each side) regardless of what shape it's formed into.

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Hi there,
If you think of a cylinder being
cut down one side and opened, it would become
a rectangle.
The circumference of the cylinder
would become either the 11 or the 8.
The height of the cylinder would be either
the 11 or the 8.
So the surface area of the outside would
equal 11 x 8 = 96 square units.
Hope this helps :-)

Question 994296: One of the new commercial airline models is 2.5 meters long and 1.2 meters wide. The width of the actual plane is 40 meters. What is it’s the actual length? Round your answer to the nearest tenth and include the units.

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.
= .

Solve for x.

Question 994237: The lengths of the sides of a triangle or consecutive even integers. Find the length of the longest side of it is 22 units shorter then the perimeter.
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The lengths of the sides of a triangle or consecutive even integers. Find the length of the longest side of it is 22 units shorter then the perimeter.
Longest side:  units



Question 994095: The measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of the other two angles and 10 degrees less than 3 times the measure of the smallest angle. Find the measures of the three angles of the triangle.
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The measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of the other two angles and 10 degrees less than 3 times the measure of the smallest angle.
Find the measures of the three angles of the triangle.
:
let the 3 angles be A, B, C, with A being the largest
:
"The measure of the largest angle of a triangle is 10 degrees more than the sum of the measures of the other two angles"
A = B + C + 10
" and 10 degrees less than 3 times the measure of the smallest angle.
A = 3C - 10
We also know that
A + B + C = 180
Rewrite the 1st equation and add to the above equation
A + B + C = 180
A - B - C = 10
--------------------Adding eliminates B and C, find A
2A + 0 + 0 = 190
A = 190/2
A = 95 degrees
Find C using the 2nd equation
A = 3C - 10
95 = 3C - 10
95 + 10 = 3C
105 = 3C
C = 105/3
C = 35 degrees
Find B
95 + B + 35 = 180
B + 130 = 180
B = 180 - 130
B = 50 degrees
:
the measures of the three angles: 95, 50, 35

Question 993983: Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.89 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 8 inches by 11 feet 8 inches. Find the area of the dining room floor, rounded up to the next square foot, and the cost of the work Answer by addingup(248) (Show Source): You can put this solution on YOUR website! OK, so 17 feet is 17x12= 204+8= 212 inches is the length And 11 feet is 11x12= 132+8= 140 inches is the width. ------------------------ The area of a rectangle is LxW= 212x140= 29,680 square inches. Now, we are talking about SQUARED numbers, right? So, 1 foot = 12 inches and 1 square foot = 12^2=144 inches. ------------------------- We said the room is 29,680 square inches, and 29,680/144= 206.11 and we round off to the nearest foot = 206 square feet. And the cost?: 206x2.89=$595.34

Question 993980: 5 Real Life Application Problem involving circles with solution. I really need your help please
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visit
http://edweb.tusd1.org/kukla/Mr_Kuklas_Website/Geometry/Worksheets/Circles/chap%20circ%20assign%2013.pdf

formula:
some more
1. An arch, in the shape of a circular arc, supports a pipeline (AB) across a river meters wide. Midway, the suspending cable (CD) is 3 meters long. Find the radius of the arch.
here is a sketch:

1.

; where segment;
;

2.
visit
http://www.shelovesmath.com/precal/parametrics-and-conics/#Circles
scroll down to
Applications of Circles
Problem:

Question 993793: How much will it cost to carpet a rectangular room measuring 19m by 25m, if carpeting costs 25.60 per square meter?
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Area of a rectangle: A = lw

A = 19 m * 25 m = 475 m^2

Cost is 25.60 * 475 = \$12,160

Question 993797: Cylinder A has a volume of 360 cm2. Cylinder B has a base and height identical to that of Cylinder B, but leans to the right in such a way that its slant length is greater by 4 cm. What is the volume of Cylinder B?
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Same volume.

Question 993674: the length of a rectangle is 1 inch less than twice that of its width. If the perimeter measures 49 inches, then find the dimensions of the rectangle.
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L = 2W - 1
P = 2L + 2W = 49
Now substituting, we get
2(2W - 1) + 2W = 49
4W - 2 + 2W = 49
Simplifying we get
6W = 51 and
W = 8.5
Then
L = 2W - 1 = 2(8.5) - 1 = 17 - 1 = 16

Question 993629: A rectangular parcel of land is 20 m wide. The length of the diagonal between the opposite corners is 5 m more than the length of the parcel. What is the length of the parcel?
Found 2 solutions by Cromlix, stanbon:
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Hi there,
Imagine you have a right angled triangle.
Width = 20 meters
Length = x
Diagonal = x + 5
(20)^2 + (x)^2 = (x + 5)^2
400 + x^2 = x^2 + 10x + 25
Collect like terms.
10x = 400 - 25
10x = 375
x = 37.5 meters
Length of parcel = 37.5 meters.
Hope this helps :-)

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A rectangular parcel of land is 20 m wide. The length of the diagonal between the opposite corners is 5 m more than the length of the parcel. What is the length of the parcel?
---
Draw the picture of the rectangle.
width = 20 m
length = x meters
diagonal = x+5 meters
----
Solve for "x"::
(x+5)^2 = x^2 + 400
----
x^2+10x + 25 = x^2 + 400
10x = 375
x = 37.5 meters (length)
------------
Cheers,
Stan H.
----------

Question 993527: A walking path around the outside of a garden is shaped like a triangle. Two sides of the path that measures 32 ft and 39 ft form a 76 degree angle. If you walk around the entire path one time, how far have you walked?
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One could recognize this as a Law Of Cosines problem.
... Is that enough help for you?

---
Let me say more thoroughly: This IS a Law of Cosines problem. You want the perimeter of the triangle, and for that, you want to find the last side of the triangle. That would be some number, say c. You have a perimeter which will be 32+39+c, and you use Law of Cosines to find c.

As a formula, Law of Cosines can be expressed in which is opposite of side c.

--
If you found c=44, then you did that part with the formula correctly. Now you should be able to evaluate the perimeter:

Question 993402: The length of a rectangle is one less than twice the rectangle's width. The rectangle's area equals 703 in^2. Find the rectangle's width (in inches)
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.
W=width; L=length=2W-1
.
A+LW
703in^2=(2W-1)(W)
703=2W^2-W
0=2W^2-W-703
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=5625 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 19, -18.5. Here's your graph:

.
ANSWER: The width is 19 inches.

Question 993342: The area of a rectangle is six square feet. The rectangle's length is two feet more than three times the width. Find the rectangle's width (in feet) rounded to two decimal places
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.
W=width; L=length=3W+2
.
A=LW
A=(3W+2)(W)
6=3W^2+2W
0=3W^2+2W-6
.
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=76 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1.11963298118022, -1.78629964784689. Here's your graph:

.
W=1.12 feet
ANSWER: The width is 1.12 feet
.
CHECK:
L=3W+2=3(1.12)+2=3.36+2=5.36
.
A=LW
6=(5.36)(1.12)
6=6

Question 993371: A rectangular garden measures 32ft by 62ft. Surrounding (and bordering) the garden is a path 4ft wide. Find the area of this path. Be sure to include the correct unit in your answer.
Found 3 solutions by MathTherapy, macston, MathLover1:
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A rectangular garden measures 32ft by 62ft. Surrounding (and bordering) the garden is a path 4ft wide. Find the area of this path. Be sure to include the correct unit in your answer.
Area of garden and path:
Area of garden:
Area of path: , or  sq ft



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.
Area of path=(area of path+area of garden)-(area of garden)
.
For area of both, garden dimensions are increased by path:
.
Area of path=(32ft+8ft)(62ft+8ft)-(32ft)(62ft)
Area of path=2800ft^2-1984ft^2=816ft^2
.
ANSWER: The area of the path is 816 square feet.

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A rectangular garden measures by ,and surrounding (and bordering) the garden is a path wide.

Question 993337: Give the dimension of the water tank, use its diagonal for the height.l = 125 cm and width = 129 cm. How to determine the diagonal of the rectangular water tank?
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the length is 125 cm.
the width is 129 cm.
the diagonal and the length and the width form a right triangle with one leg = 125 cm and the other leg = 139 cm.
the diagonal is equal to sqrt(125^2 + 129^2) = 179.6273921 cm

you are using the pythagorian formula of a right triangle which is:
H^2 = L1^2 + L2^2
H is the hypotenuse
L1 is one of the legs of the right triangle.
L2 is the other leg of the right triangle.
take the square root of H^2 and you have H.

Question 993301: Dave wants to make a stone walkway. The rectangular walkway is 4 feet wide by 12 feet long. Each 2 foot by 2 foot stone covers an area of 4 square feet. How many stones will Dave need to cover his walkway?

Found 2 solutions by MathTherapy, josgarithmetic:
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Dave wants to make a stone walkway. The rectangular walkway is 4 feet wide by 12 feet long. Each 2 foot by 2 foot stone covers an area of 4 square feet. How many stones will Dave need to cover his walkway?
Each 2 ft by 2 ft stone covers an area of 4 sq ft
Area needed to be covered: 4(12), or 48 sq ft
Number of stones needed: , or



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Area of walkway, square feet
Area of 1 stone, square feet

Question 993266: the distance from a man to the top level of a vertical building standing on the level ground measured along his line sight is 29m. The man lies on the ground with his head 21m from the base of the building. Determine the hieght of the building
neglecting the hieght of the man

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Per Pythagoras:
29^2-21^2= h^2
841-441= 400 Take the square root of 400
√400= 20 is the height of the building

Question 993175: two cylindrical ice pillars will flank the front door. Each cylinder has a diameter of 1 foot and height of 9 feet. The ice weighs 62.4 pounds per cubic feet.
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Hi there,
I assume that you are looking for the total weight
of these cylinders.
Formula:Volume = Pi x r^2 x h
Volume = Pi x 0.5^2 x 9
Volume = 7.069 ft^3
At 62.4 pounds per cubic foot
The weight of one cylinder =
62.4 x 7.069
= 441.11 pounds per cylinder
or 882.22 pounds for two cylinders.
Hope this helps :-)

Question 993023: The area of rectangle is 120. If one side is 2 longer than the other side eWhatis the perimeter of the rectangle?
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The sides or dimensions may be x and x+2, so the area is . Can you do the rest? Quadratic equation in x.

Question 992949: the length of a triangle is 3 meters less than twice its width> Write an equation to find the length of the triangle
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.
the length of a triangle ??

Question 992859: Two sides of a triangle are 3ft and 6ft longer then the third side. If the perimeter of the triangle is 36ft find the lenght of each side
Found 2 solutions by Alan3354, lwsshak3:
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x + x+3 + x+6 = 36
3x + 9 = 36
3x = 27
x = 9
===============
---> 9, 12 & 15
P = 36

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Two sides of a triangle are 3ft and 6ft longer then the third side. If the perimeter of the triangle is 36ft find the lenght of each side
let x= length of3rd side
x+3=2nd side
x+6 =1st side
2(x+3+x+6)=36
4x+18=36
4x=18
x=4.5
x+3=7.5
3rd side=4.5 ft
1st side=7.5 ft
2nd side= 10.5 ft

Question 992777: Two missiles are fired simultaneously from the same location to different directions. Their speeds are 75.39m/s and 83.26m/s. The angle between their locations is 62.19 degrees. How far are the missiles after 0.75 sec?
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Use cosine rule after calculating the distance travelled by each missile in 0.75 sec.

Question 992778: Two side of a triangle are 50m and 60m long. The angle included between these sides are 30 degrees, what is the interior angle opposite the longest side?
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Let us use the cosine rule first.
a = 50
b = 60
C = 30 degrees

So largest side is b = 60 m.

Using Sine rule

B = 86.3 degree

Question 992780: Two sides of a triangle are a = 23.9m and b = 36.3 m the angle opposit side b is 102.7 degrees. Determine the length of side c.
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Two sides of a triangle are a = 23.9m and b = 36.3 m the angle opposit side b is 102.7 degrees. Determine the length of side c.
----------------
Use the Sine Law to find angle A.
sin(A)/a = sin(B)/b
---
Then find angle C.
Then find c using the Cosine Law.
------
email via the TY note for help or to check your work.

Question 992768: Galileo Galilei conducted experiments involving Italy’s famous Leaning Tower of Pisa to investigate the relationship between an object’s speed of fall and its weight. The Leaning Tower is 804 ft. shorter than the Eiffel Tower in Paris, France. The two towers have a total height of 1,164 ft. How tall is each tower?
Found 2 solutions by stanbon, Cromlix:
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Galileo Galilei conducted experiments involving Italy’s famous Leaning Tower of Pisa to investigate the relationship between an object’s speed of fall and its weight. The Leaning Tower is 804 ft. shorter than the Eiffel Tower in Paris, France. The two towers have a total height of 1,164 ft. How tall is each tower?
----
LT = ET-804
LT + ET = 1164
------
ET-804 + ET = 1164
2*ET = 1908
ET = 954 ft (height of Eiffel Tower)
LT = 954-804 = 150 (height of Leaning Tower)
============
Cheers,
Stan H.
-------------

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Hi there,
Assume that the Eiffel Tower = 'x'
Leaning Tower = x - 804.
Therefore:
x + (x - 804) = 1,164 ft
x + x - 804 = 1,164 ft
2x - 804 = 1,164
2x = 1,164 + 804
2x = 1,968
x = 984 ft
Eiffel Tower = 984 ft
The Leaning Tower = 180 ft
Hope this helps :-)

Question 992709: http://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.215278.html
Where does the x=36 come from?

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Remove parenthesis

Combine like terms

Rewrite 2x as

Multiply both sides by 3.

Divide both sides by 10.

Question 992571: Cynthia Besch wants to buy a rug for a room that is 18 feet wide and 19 feet long. She wants to leave a uniform strip around the rug. She can afford 272 square feet of carpeting. What dimensions should the rug have?
272+(19-2x)(18+2x)
1, 35/2
But, what are the dimensions in feet? How do I convert? Thanks.

Found 2 solutions by vleith, rothauserc:
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Let the width of the strip be x
The rug will have square footage of (18-2x)*(19-2x)
you are told she wants a rug that is 272 sq ft
so

 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=4356 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 17.5, 1. Here's your graph:

so the strip will be 1 ft wide
That makes the rug (18-2) by (19-2) feet
16 feet by 17 feet

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The border will be inside the dimensions of the room, therefore
(19-2x) * (18-2x) = 272
342 - 74x + 4x^2 = 272
rearrange the terms
4x^2 - 74x + 342 = 272
divide both sides of = by 4
x^2 - 18.5x + 85.5 = 68
subtract 68 from both sides of =
x^2 - 18.5x + 17.5 = 0
use quadratic formula to solve for x
x = (-(-18.5) + sqrt((18.5^2)−(4×17.5))) / 2 = 17.5
x = (-(-18.5) - sqrt((18.5^2)−(4×17.5))) / 2 = 1
****************************************************************
The reasonable dimension for the strip around the rug is 1 foot, therefore
the dimensions for the rug are 17 feet long and 16 feet wide

Question 992520: the size of each tile in the room is 50cm by 50 cm

calculate the areas of each tile

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Hi dear,
Since the tiles measure 50cm by 50cm,/hen the shape of each tile is a square
The area of
each tile= 50cm*50cm=2500cm²
HOPE THIS HELPS?

Question 992518: suppose one of your rooms is measured in 5m by 8m
calculate the areas of a room

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Hi dear,
If the room measure 5m by 8m,
This means that the lenght and the width is 5m and 8m respectively
Now the Flow of your room is in the shape of rectangle.
From the above,
Area A of the room=5m*8m
=40m²
HOPE THIS HELPS?

Question 992131: The length and breadth of a page of my exercise book is 15 cm and 12 cm. A margin of width 2 cm is drawn on all sides and wrote inside the margin. Find the area of portion on which I wrote and also find the area of the portion on which I have not written

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The overall area of the page is the product of the length and width of the page. The area of the page containing writing is the length of the page minus 2 times the width of the margin times the width of the page minus 2 times the width of the margin. The area of the margin is the total area of the page minus the area of the page containing writing.

John

My calculator said it, I believe it, that settles it

Question 992298:
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.
Empty request goes into trash.

Question 992352: Algebra 2 word problem:
The width of the rectangle is 3 feet less than its length. The perimeter of the rectangle is 110 feet. Find its dimensions.

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The width of the rectangle is 3 feet less than its length. The perimeter of the rectangle is 110 feet. Find its dimensions.
---
length:: x
width::: x-3
----
P = 2(length + width)
110 = 2(x + x-3)
55 = 2x-3
2x = 58
x = 29 (width)
x-3 = 26 (length)
-----------
Cheers,
Stan H.
----------

Question 992332: Construct a 8cm^2 square using a 4cm^2 square. Thank you!
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.
Use the diagonal of the given square as the side of the larger square that you need to construct.

The diagonal of the given square is .

So the square of the diagonal is = 8.

It is the area of the square you need to construct.

Question 992171: A picture frame (see figure) has a total perimeter of 4 feet. The width of the frame is 0.63 times its length. Find the dimensions of the frame. (Round your answers to two decimal places.)
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.
L=length; W=width=0.63L
.
P=2(L+W)
4ft=2(L+0.63L)
2ft=1.63L
1.23ft=L ANSWER 1: The length is 1.23 feet.
.
W=0.63L=(0.63)(1.23ft)=0.77ft
ANSWER 2: The width is 0.77 feet
.
CHECK:
P=2(L+W)
4ft=2(1.23ft+0.77ft)
4ft=2(2ft)
4ft=4ft

Question 992057: What is .3 repeating a natural, whole, integers, rational. Irrational