Questions on Geometry: Rectangles answered by real tutors!

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Question 571187: the length of a rectangle is 6inch less than twice its width. If the perimeter of the rectangle is 72inches, find the dimesions of the rectangle. Please help use the simplest way to solve this problem because I am not good in algebra and I know this has a little algebra in it.
Found 2 solutions by Theo, mrjunecarlo1095@ymail.com:
Answer by Theo(2960)   (Show Source):
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let L equal the length of your rectangle.
let W equal the width of your rectangle.
let P equal the perimeter of your rectangle.
the formula for the perimeter of a rectangle is 2L + 2W = P
since P equals 72, this formula becomes:
2L + 2W = 72
you are also given that L = 2W - 6
this equation says that the length of the rectangle is 6 inches less than twice the width.
you can substitute for L in the equation of:
2L + 2W = 72 to get:
2(2W-6) + 2W = 72
you simplify this equation to get:
4W - 12 + 2W = 72
you combine like terms to get:
6W - 12 = 72
you add 12 to both sides of this equation to get:
6W = 72 + 12
you combine like terms to get:
6W = 84
you divide both sides of this equation by 6 to get:
W = 84 / 6
you simplify this to get:
W = 14
since L = 2W - 6, this means that:
L = 2*14 - 6 which becomes:
L = 28 - 6 which becomes:
L = 22
you have:
L = 22 inches
W = 14 inches
going back to the original formula of:
2L + 2W = 72, you have:
2*22 + 2*14 = 72 which becomes:
44 + 28 = 72 which becomes:
72 = 72
this confirms the values for L and W are good.
your length is 22 inches.
your width is 14 inches.

Answer by mrjunecarlo1095@ymail.com(4)   (Show Source):
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Let L be length: L = 2W-6
W be width : W = W
Perimeter is 72 inches.
Formula of Perimeter of a Rectangle: P=2L+2W
easily substitute L = 2W-6 to Length ,and W = W to Width
So, P= 2L+2W
by substitution P=72
72 = 2(2W-6) + 2W
72 = 4W - 12 +2W
72 + 12 = 6W
86 = 6W
so,
W= 14
and subs the value of W to L
L= 2W -6
= 2 (14) -6
= 28 - 6
= 22
Th answer is 22 by 14.

Question 571188: what hapens to the perimeter of a rectangle if we multiply both its length and widht by 2? by 3? by 10? by n? I really don't know where to start here.
Answer by stanbon(48502)   (Show Source):
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what hapens to the perimeter of a rectangle if we multiply both its length and widht by 2? by 3? by 10? by n? I really don't know where to start here.
---
Start with the formula:
P = 2(L+W)
---
P/2 = (L+W)
====
Now double length and width:
Multiply both sides by 2 to get:
P = (2L+2W) ; The perimeter doubled
---
Multiply both sides by 3 to get:
3(P/2) = 3L + 3W : The perimeter is multiplied by 3
etc.
Cheers,
Stan H.
============

Question 571190: Suppose two rectangles both have a perimeter of 40 m. Must they also have the same area? Try several examples to test your conjecture.
Answer by stanbon(48502)   (Show Source):
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Suppose two rectangles both have a perimeter of 40 m. Must they also have the same area? Try several examples to test your conjecture.
---
Try it with length = 8 and width = 12
Try it with length = 10 and width = 10
----------------------------------
Cheers,
Stan H.

Question 571090: The area of a rectangle is 112 meters squared. The width is 8 meters. What is the length of the rectangle? I cannot figure this out. Please help!
Answer by Alan3354(21541)   (Show Source):
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The area of a rectangle is 112 meters squared. The width is 8 meters. What is the length of the rectangle?
--------------
Area = L*W
L = Area/W

Question 571067: The length of a rectangular garden is 4 yd greater than the width. The area of the garden is 96 〖yd〗^2.Find the length and the width.
Answer by mananth(10539)   (Show Source):
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width of garden = x yards
Length of garden = x+ 4 yards

Area = L*W
Area= 96 sq. yards
Area = x(x+ 4 )
x(x+ 4 )= 96

x^2 + 4 x = 96
x^2 + 4 x -96 = 0
x^2+ 12 x -8 x - -96 = 0
x(x+ 12 ) -8 (x+ 12 )= 0
(x+ 12 )(x -8 )= 0

x= -12 OR 8
Ignore negative.
so x= 8
Width 8 yards
Length 12 yards (width + 4 )
m.ananth@hotmail.ca

Question 570926: The length of a rectangle is 4 inches more than three times the width. The perimeter is 88 inches. Find the length and width.
Answer by Maths68(1140)   (Show Source):
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Perimeter = p = 88 inches
Width = w = ?
Length = l = 3w+4

Perimeter of rectangle = 2 (l+w)
Put l = 3w+4
p=2(3w+4+w)
88=2(4w+4)
88/2=2(4w+4)/2
44=4w+4
44=4(w+1)
44/4=4(w+1)/4
11=w+1
11-1=w
10=w

Perimeter = p = 88 inches
Width = w = 10 inches
Length = l = 3w+4 = (3)(10)+1 = 30+4 = 34 inches

Question 570228: the area of the floor of a rectangular room is 84 square feet. the length of the room is 5 ft more than the width. Find the length and width
Answer by Alan3354(21541)   (Show Source):
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the area of the floor of a rectangular room is 84 square feet. the length of the room is 5 ft more than the width. Find the length and width
-----
If you factor 84, you'll find it has a factor of 7.

Question 570211: write the equation of a line that has a slope of 5/2 and passes through (2,3).
Answer by nerdybill(5399)   (Show Source):
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write the equation of a line that has a slope of 5/2 and passes through (2,3).
.
Plug given info into the "point-slope" form:
y - y1 = m(x - x1)
y - 3 = (5/2)(x - 2)
y - 3 = (5/2)x - 5
y = (5/2)x - 2 (this is what they're looking for)

Question 570204: the perimeter of a rectangle is 54 m. The width is 3 m less than twice the length. Find the dimensions of the rectangle?
Answer by JBarnum(1826)   (Show Source):
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GIVEN:
2W+2L=P
P=54
W=2L-3
,
SOLVE:
substitution
2(2L-3)+2L=54
4L-6+2L=54
6L=60
L=10
.
W=2L-3
W=2(10)-3
W=20-3
W=17

Question 569975: If I have a height of 15ft. and an area of 285ft.^2 what is the missing dimension.
Answer by JBarnum(1826)   (Show Source):
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length or width depending on the side your area is for

Question 569914: how do you find the are of a square when you have the perimeter ?
Answer by JBarnum(1826)   (Show Source):
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area is length times width
since its a square all sides are same so it would be
where peremeter is

Question 570099: A rectangle is 3cm longer and 2cm less in width than a certain square. The area of the rectangle is 16cm^2 greater than the area of the square. What is the length of the rectangle?
Answer by JBarnum(1826)   (Show Source):
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(x+3)(x-2)=16+x^2
x^2+x-6=16+x^2
x-6=16
x=10
rectangle length=x+3
so 10+3=13

Question 411091: New playground will be rectangler and have an area of 225 yrds 2. The number of yards on each side will be a whole number. What is the least amount of fencing that could be required to enclose the playground?
I have a picture that has anh area of 3,600 cm2 and is square. I have a picture frame that is 5 cm wide. What is the perimeter of the picture frame?
Answer by childress(1)   (Show Source):
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Question 570063: a rectangle has a length of 17 inches more than three times its height if the perimeter is 498 what are the deminsions
Answer by rfer(10417)   (Show Source):
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2(3x+17)+2x=498
6x+34+2x=498
8x=498-34
8x=464
x=464/8
x=58
3x+17=191

Question 569997: is there Rectangle with 4 square cm and perimeter 10
Answer by AnlytcPhil(1116)   (Show Source):
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LW = 4 2L + 2W = 10 Divide the second equation by 2 L + W = 5 Solve for L L = 5 - W Substitute in LW = 4 (5 - W)W = 4 5W - W² = 4 -W² + 5W - 4 = 0 Multiply through by -1 W² - 5W + 4 = 0 (W - 4)(W - 1) = 0 W - 4 = 0; W - 1 = 0 W = 4; W = 1 L = 5 - W L = 5 - W L = 5 - 4 L = 5 - 1 L = 1 L = 4 So either a 1cm x 4cm or a 4cm x 1 cm rectangle. Either of these, which are draw to scale: Edwin

Question 569951: if a golden rectangle has a length of 234 meters, what would its width need to be?
Answer by rfer(10417)   (Show Source):
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ratio 1:1.618
234/1.618=145 meters

Question 569690: write an expression for 81 fewer than the product of u and 158

Answer by unlockmath(1118)   (Show Source):
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Hello,
We would write this as:
158u-81
Make sense?
RJ
www.math-unlock.com

Question 569661: ?what is x?
Answer by JBarnum(1826)   (Show Source):
You can put this solution on YOUR website!

find common denom fastest is to just multiply the two denoms
20*16=320
16*7=112
20*3=60
add
reduce by 4 172/4=43 320/4=80

Question 569645: x= 5/6 - 2/7 ?what is x?
Answer by Alan3354(21541)   (Show Source):
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x= 5/6 - 2/7 ?what is x?
---------
x = 35/42 - 12/42
x = 23/42

Question 569576: The lid of a rectangular box of side 40 cm by 10 cm is sealed all round with tape. what is the length of the tape required?
Answer by nerdybill(5399)   (Show Source):
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The lid of a rectangular box of side 40 cm by 10 cm is sealed all round with tape. what is the length of the tape required?
The length of the tape would be equivalent to the perimeter:
2(40 + 10)
2(50)
100 cm

Question 569484: The perimeter of a rectangle is 36 cm. The length of the rectangle is 3 cm more than twice the width. What are the dimensions of the rectangle?
Answer by bluemockingjay7(41)   (Show Source):
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perimeter = 36cm
length = 2x + 3
width = x
2x + 3 + x = 36
2(2x + 3 + x) = 36
4x + 6 + 2x = 36
6x = 30
6x/6 = 30/6
x = 5
width = 5 cm
length = 2(5) + 3 = 13 cm

Question 569370: DEFG is a square with diagonals GE and DF. If GE=10-2x and DF=2+2x find the value of x
Answer by IWork4Dessert(57)   (Show Source):
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Since you know that DEFG is a square, you also know that both its diagonals are going to be equal. All you have to do here is set up an equation and solve it.
10-2x=2+2x
Subtract 2 from both like terms.
8-2x=2x
Add 2x to the other side to get the variable alone.
8=4x
Divide both sides by 4.
x=2
Hope this helps(:

Question 569358: if a rectangle has a perimeter of 36 inches and length of 5 inches what is the area

Answer by IWork4Dessert(57)   (Show Source):
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What do you know about rectangles? In order for a shape to be a rectangle, it has to have two pairs of equal sides. You can start by drawing one up(I'm afraid I can't draw one in this text box, so bear with me).
First of all, you know that the length of one of the sides is 5. But if a rectangle has two pairs of equal sides, then the length opposite that one will be 5 as well. Go ahead and label those.
Now. You know that the perimeter is 36. Perimeter is all of the sides added together. The sides we don't know the lengths of are going to be equal too, like I said above. Two of the sides together(5+5) are 10. Your equation:
36=10+2x
Now subtract 10 from both sides(remember, you're trying to get the variable--the letter--alone).
26=2x
Divide both sides by 2 to get the variable by itself.
13=x
Since the problem is asking for the area, all you have to do is multiply the short side(5) by the long side(13).
5x13=65
65 inches squared

Question 569323: the length of a rectangle is 7 inches longer than its width if the area of the rectangle is 144 square inches what are its demensions?
Answer by solver91311(12114)   (Show Source):
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but in this case

So:

And in this case,

So:

or, in standard quadratic form:

Solve the quadratic for , discard the extraneous negative root, then calculate .

Hint: The quadratic factors.

Hint: 16 minus 9 is 7.

John

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

Question 569291: Here is my question.
You have a rectangle with 78 square centimeters.What are the dimensions of the rectangle with the largest perimeter?
Im not so sure about how to do this. Please help!
Answer by stanbon(48502)   (Show Source):
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You have a rectangle with 78 square centimeters.What are the dimensions of the rectangle with the largest perimeter?
------
Equation:
LW = 78 sq. cm
Perimeter = 2(L + W)
---
P = 2(L + (78/L))
---
P = 2(L^2+78)/L
---
P = (2L^2+156)/L
---
Take the derivative:
P' = [L(4L)-(2L^2+156)]/L^2
------
P' = [2L^2-156]/L^2
-----
Solve: P' = 0
---
2L^2-156 = 0
L^2 = 78
Length = sqrt(78)
-----
Width = sqrt(78)
=======================
Cheers,
Stan H.
===============

Question 569217: Can someone help me with this question: A rectangle animal pen will be built using 200 meters of fencing. If one side of the rectangle is 60meters, find the area of the pen.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(21541)   (Show Source):
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Can someone help me with this question: A rectangle [sic] animal pen will be built using 200 meters of fencing. If one side of the rectangle is 60meters, find the area of the pen.
-----------
Hint:
Perimeter = 2(L + W) = 200
L + W = 100
----
Area = L*W

Answer by stanbon(48502)   (Show Source):
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A rectangle animal pen will be built using 200 meters of fencing. If one side of the rectangle is 60meters, find the area of the pen.
-----
Draw the rectangle.
Label one side as 60 meters.
---
Then the side opposite is also 60 meters.
Label both of the other sides as "x":
Equation:
Perimeter = (each of the 4 sides)
200 = 2*60+2x
---
100 = 60 + x
x = 40 meters.
---
Area = 40*60 = 2400 sq. ft.
=============================
Cheers,
Stan H.
=============================

Question 568692: Find the dimension of a rectangular Persian rug whose perimeter is 18 ft. and whose area is 20 ft^2?
what are the length and width?
Answer by stanbon(48502)   (Show Source):
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Find the dimension of a rectangular Persian rug whose perimeter is 18 ft. and whose area is 20 ft^2?
what are the length and width?
-------------------------------------
Perimeter = 2(L + W)
----------------
L+W = 9
LW = 20
-----
L = 9-W
----
Substitute for "L" and solve for "W":
(9-W)W = 20
-W^2+9W = 20
---
W^2-9W+20 = 0
-----
(W-5)(W-4) = 0
If W = 5, L = 4
If W = 4, L = 5
========================
Cheers,
Stan H.
=============

Question 568544: find area of a quadrilateral with the given dimensions
L=5M W=7M A=_______M2
Answer by issacodegard(60)   (Show Source):
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Question 568504: By decreasing the length of the side by one unit, the area of a square decreased from 100 square meters to 81 square meters. Find the percent decrease in area.
Answer by jim_thompson5910(21667)   (Show Source):
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(100-81)/(100) = 19/100 = 0.19

So the percent decrease is 19%
-------------------------------------------------------------------------------------------------
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Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 568305: A rectangle has a width of 3X inches and a length that is 8 inches shorter. The area is 825 sq. inches find the dimensions.
X_____, W__________,L____________, Perimeter________
Answer by mananth(10539)   (Show Source):
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Width = 3x
Length = 3x-8
Area = L*W
825 = 3x(3x-8)
825=9x^2-24x
9x^2-24x-825=0
Find the roots of the equation by quadratic formula

a= 9 , b= -24 , c= -825

b^2-4ac= 576 + 29700
b^2-4ac= 30276

x1=( 24 + 174 )/ 18
x1= 11.00
x2=( 24 -174 ) / 18
x2= -8.33
Ignore negative value
x = 11
width = 3x = 33 inches
Length = 3x-8 , 33-8=25 inches
Perimeter = 2(L+W)
you can work that out

CHECK
33 * 25 = 825

m.ananth@hotmail.ca

Question 568282: the length of a rectangular greenhouse is three times the width. if the perimeter of the greenhouse is 96 feet, what are the dimensions of the greenhouse?
Answer by TutorDelphia(189)   (Show Source):
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They tell you that L equals 3 times W:
l=3w
The formula for perimeter is just to add up all the sides (2 sides are the length and 2 are the width)
2l+2w=96
we can divide both sides by 2 and get
l+w=48
we know l=3w so we can sub that in
3w+w=48
combine like terms
4w=48
divide both sides by 4
w=12
l=3*12
l=36

Question 568308: If a square of "x" is cut out of a rectangle whose dimensions are 10 by 12, express the remaining area in terms of "x"
Answer by TutorDelphia(189)   (Show Source):
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The remaining area will just be the current area minus how much is cut out.
Its hard to tell from your working if x is the side or x is the area. If x is the area you just get
r=120-x where r is the remaining area, 120 is the current area and x is the area of the square
if its the side than you have
since the area of a square is just the side squared.

Question 567934: The length of a room is 4 m and it's breadth is 3 m. How many square tiles of side 20 cm are required to cover the floor of the room?
Answer by mananth(10539)   (Show Source):
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Area of room/area of tile = number of tiles
Area of room = 4*3 = 12 m^2
Area of tile = ).2*0.2 = 0.04 m^2
12/0.04
300 tiles

Question 567837: The perimeter of a standard rectangle is 24ft rug the length is 2ft longer than the width what is the wdth? What is the length
Answer by rapaljer(4551)   (Show Source):
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Let x = width of the rectangle
x+2 = length of the rectangle

2W + 2L = Perimeter
2(x) + 2(x+2) = 24
2x + 2x + 4 = 24
4x + 4 = 24
4x= 20
x = 5 ft width
x+2= 7 ft length

Check: 2*5 + 2*7=24 ft.

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Seminole State College of Florida
Altamonte Springs Campus

Question 567623: one integer is less than the other. the product of the two intergers is 60. what is one of the numbers?
Answer by richard1234(4787)   (Show Source):
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You can't really solve for the integers because there are many different solutions (since you stated "one integer is less than the other" which obviously happens unless we have a perfect square). For example 5*12 = 60, 2*30 = 60, etc.

Question 567535: If the perimeter of a regtangle is 80m and the area is 300 m2 what is the length and width of the rectangle. What is the formula for working out this?
Answer by mananth(10539)   (Show Source):
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perimeter of recatngle = 2(L+W)
2(L+W)=80
Area of rectangle = L*W
L*W= 300
L= 300/w
substitute L in the first equation

Multiply by W

divide by 2

W(W-30)-10(W-30)=0
(W-30)(W-10)=0
W= 30 OR 10
The dimensions are 30m by 10m
m.ananth@hotmail.ca

Question 567007: If I have 40ft or material for the perimeter of a sandbox, what is the smallest area I can have the sides have to be in whole numbers so no mixed numbers or fractions.
Answer by solver91311(12114)   (Show Source):
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I don't think you meant "the smallest area" because the answer is absurd. The smallest area is zero square feet. You just cut your material in half and have a 20 foot by 0 foot non-sandbox.

John

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

Question 566968: If I have a rectangle of 24 meter square which can not be the length of one of it's sides,22 meter or 28 meters? I say 28 meters because the other side would be .8567823
Answer by solver91311(12114)   (Show Source):
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No, if one side measured 28, then the other side would measure , but there is nothing wrong about that value as the measure of the side of a rectangle. It certainly isn't any more or less correct than .

John

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

Question 566791: How do I find h & w when h is 7 more than w, and I am only given the area of 330ft^2?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(48502)   (Show Source):
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How do I find h & w when h is 7 more than w, and I am only given the area of 330ft^2?
-------
Let width = w
Then height = (w + 7)
----
Area = width*height = 330 ft^2
-----
w^2+7w-330 = 0
---
Factor:
(w-15)(w+22) = 0
---
Width = 15 ft
Height = 15+7 = 22 ft
===========================
cheers,
Stan H.
==================

Answer by solver91311(12114)   (Show Source):
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You are not "only given the area...", you are also given that is 7 more than .

You also know that the area is given by , so substitute:

And with the given value for area:

Put it in standard form:

Solve the quadratic (it factors, 22 and 15 have a difference of 7, hmmm), discard the negative root. The positive root is and is 7 more than that.

John

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

Question 566110: I am in a refresher math course and remember having to do things in parentheses first but not sure what next. This is the problem 5 + [4 + (12-4) divided by 2 ] .I got 4 but I'm not sure if this is correct .can you please help ,I'd greatly appreciate it. Thank you.
Answer by jcarena(2)   (Show Source):
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In mathematics and computer programming, the order of operations (sometimes called operator precedence) is a rule used to clarify unambiguously which procedures should be performed first in a given mathematical expression.
Parenthesis, Exponent, Multiplication, Division, Add, and Subtraction also known
as: Please Excuse My Dear Aunt Sally (PEMDAS)

5 + [4 + ( 12-4) ÷ 2]
= 5 + [4 + (8)÷ 2 ]
= 5 + [ 4 + 4 ]
= 5 + 8
= 13

Question 566102: What would the area be of 22 miles in width and 13 miles in length?
Answer by Alan3354(21541)   (Show Source):
You can put this solution on YOUR website!
What would the area be of 22 miles in width and 13 miles in length?
-------------
If it's a rectangle,
Area = W*L
----------
= 286 sq miles

Question 565972: I really need your help!
The length of a rectangle is 3ft less than 2 times the width. What is the length and width if the perimeter is 42?
Answer by ad_alta(170)   (Show Source):
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Let 'l' be the length and 'w' the width. Then l=2w-3. Also, 42=2w+2l. Substituting the first equation into the second we get 42=2w+2(2w-3). Solving, we get w=8 and l=13.