# Questions on Geometry: Rectangles answered by real tutors!

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Question 817552: how to do this problem?
the perimeter of a rectangle is 28 cm. one side is 10 cm longer than the other side. find the lengths of the sides.

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2L + 2w = 28
L = w + 10
---
2L + 2w = 28
2(w + 10) + 2w = 28
2w + 20 + 2w = 28
4w = 8
---
w = 2
L = 12
---
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Question 817469: the perimeter of a rectangle is 42m.the length is 9m less than two times the width. what is length and the width of the rectangle

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2L + 2w = 42
L = 2w - 9
---
2L + 2w = 42
2(2w - 9) + 2w = 42
4w - 18 + 2w = 42
6w = 60
---
w = 10
L = 11
---
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Question 817442: The perimeter of a rectangle is 256. The length is 3 times the width. What are the length and width of the rectangle?
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2L + 2w = 256
L = 3w
---
2L + 2w = 256
2(3w) + 2w = 256
6w + 2w = 256
8w = 256
---
w = 32
L = 96
---
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Question 817437: can i get a 34"x 21" rectangle through a 32"x 33" opening?
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Yes. The short side of the rectangle is 21". That fits through the opening which is 32" wide and 33" high. 21" < either of those dimensions.

Question 817440: whats the perimeter of a rectangle with the length is 25 cm and the area is 200 square inches
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Hi,
whats the perimeter of a rectangle with the length is 25 cm 0r
and the area is 200 square inches

A = Lw 0r w =
P =

Question 817042: [ What is the simplest form of (5x) / (25x)? ]
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(5x) / (25x)
(5) / (25)
1 / 5
---
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Question 817038: A rectangular window has a perimeter of 258 inches. The width of the window is 24 inches. What is the area of the window?
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p = 2L + 2w = 258
w = 24
---
2L + 2w = 258
2L + 2(24) = 258
2L + 48 = 258
2L = 210
---
L = 105
---
a = Lw
a = 105 * 24
---
a = 2520 sq.in
---
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Question 816886: The perimeter of a rectangle is 40 centimeters.
One side is 5 centimeters.
What is the length of the other side?
What is the area of it?

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15 is the other side
15+15+5+5=40
15*5=75 area

Question 816789: a rectangle has a perimeter of 28cm and width of 5cm what is its length?
You can put this solution on YOUR website!

Hi,
a rectangle has a perimeter of 28cm and width of 5cm what is its length 'L'?

P =
2L = 18cm
L = 9cm . length is 9cm

Question 816742: the area (in ft2) of a rectangle that is three times as long as it is wide; w= width of the rectangle (in cm).
You can put this solution on YOUR website!

Hi,
rectangle that is three times as long as it is wide;
w= width of the rectangle (in cm)
A(in cm^2) =
A(in ft^2) = | 1 ft^2 = 929.0304 cm^2

Question 816660: [ A long wire is cut into three smaller pieces in the ratio of 7:3:2. if the shortest piece is 16 cm, what is the area of the rectangle with the largest area that can be created using the longest piece? ]
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a = (7/12)L
b = (3/12)L
c = (2/12)L
---
c = 16 cm
c = (2/12)L
16 = (2/12)L
---
L = 16(12/2)
L = 96 cm
---
a = (7/12)L
a = (7/12)96
a = 56 cm
---
b = (3/12)L
b = (3/12)96
b = 24 cm
---
a is the longest piece at 56 cm
---
what is the area of the rectangle with the largest area that can be created using the longest piece?
it's actually a square, so:
L = w = (1/4)56
L = w = 14
a = Lw = 14^2
a = 196 sq.cm
---
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Question 816657: The length of a rectangle is twice its width.
If the perimeter of the rectangle is 54 m , find its area

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L = 2w
p = 2L + 2w = 54
---
2L + 2w = 54
2(2w) + 2w = 54
4w + 2w = 54
6w = 54
w = 9
L = 2w = 18
---
a = Lw
a = 18 * 9
---
a = 162 sq.m
---
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Question 816592: Six times the diference of a number and 9 is less than the number
You can put this solution on YOUR website!
the difference of a number and 9

6 times this....multiply all of it by 6

is less than the number

now solve for n

dividing by a negative number flips the sign ***you must do this***

Question 816588: Find the lenght of a rectangle if its width is 13 less than the lenght and its perimeter 90cm
You can put this solution on YOUR website!
p = 2L + 2w
90 = 2L + 2(13)
---
2L = 90 - 2(13)
2L = 90 - 26
2L = 64
---
L = 32 cm
---
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Question 816561: how to connect two similer rectangles in breathwise

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how to connect two similer rectangles in breathwise
--------
idk what that means.

Question 816556: [ the hypotenuse of a triangle is 14 in. if the base of the triangle is 2 in determine the length of the remaining side ]
You can put this solution on YOUR website!
h = sqrt( b^2 + L^2 )
14 = sqrt( 2^2 + L^2 )
14^2 = 4 + L^2
L^2 = 196 - 4
L^2 = 192
---
L = 13.856406 in
---
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Question 816549: [ The length of the rectangle is 8 centimeters less than twice the width. The area of the rectangle is 24 centimeters squared. Determine the dimensions of the rectangle in centimeters ]
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L = 2w - 8
Lw = 24
---
Lw = 24
(2w - 8)w = 24
2w^2 - 8w - 24 = 0
---
---
the above quadratic equation is in standard form, with a=2, b=-8, and c=-24
---
to solve the quadratic equation, plug this:
2 -8 -24
---
the roots of the quadratic are:
w = 6
w = -2
---
the negative root doesn't make sense for a length, so use the positive root
---
w = 6 cm
L = 4 cm
---
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Question 816529: find the area of a square whose perimeter is 7 meters
You can put this solution on YOUR website!
7/4=1.75
1.75^2=3.0625 sq m

Question 816341: A rectangle is drawn so the width is 71 inches longer than the height. If the rectangle's diagonal measurement is 85 inches, find the height.

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w = h + 71
d = 85 = sqrt( ww + hh )
---
85 = sqrt( ww + hh )
85^2 = ww + hh
85^2 = (h + 71)(h + 71) + hh
85^2 = hh + 142h + 71^2 + hh
2h^2 + 142h + 71^2 - 85^2 = 0
2h^2 + 142h - 2184 = 0
---
the above quadratic equation is in standard form, with a=2, b=142, and c=-2184
---
to solve the quadratic equation, plug this:
2 142 -2184
---
the roots of the quadratic are:
h = 13
h = -84
---
the negative root doesn't make sense for a length, so use the positive root
---
h = 13 in
w = 84 in
---
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Question 816293: The area of a rectangle is 33m squared, and the length of the rectangle is 5m less than twice the width. Find the dimensions of the rectangle.
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a = Lw = 33 sq.m
L = 2w - 5
---
Lw = 33
(2w - 5)w = 33
2w^2 - 5w - 33 = 0
---
the above quadratic equation is in standard form, with a=2, b=-5, and c=-33
---
to solve the quadratic equation, plug this:
2 -5 -33
---
the roots of the quadratic are:
w = -3
w = 5.5
---
the negative root doesn't make sense for a length, so use the positive root
---
w = 5.5 m
L = 6.0 m
---
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Question 816203: what are the measurements of (1/3)rd of a foot scale in the (a)inches and the (b)centimeter units respectively?
You can put this solution on YOUR website!

Hi,
(1/3)rd of a foot scale
Note: 1 in = 2.54cm
and 4in =

Question 816093: A rectangle has an area of 75 square inches. The length of the rectangle is three times as long as the width of the rectangle. Find the dimensions of the rectangle?
You can put this solution on YOUR website!
x = width
3x = length {the length is 3 times the width}

Area of a rectangle = width x length

x(3x) = 75 {substituted width, length, and area into area formula}
3x² = 75 {multiplied}
x² = 25 {divided each side by 3}
x = 5 {took square root of each side}
3x = 15 {substituted 5, in for x, into 3x}

width = 5 inches
length = 15 inches

For more help from me, visit: www.algebrahouse.com

Question 815887: the width of a rectangle is 2 meters less than the length. the area is 48 square meters. find the dimensions of the rectangle.
You can put this solution on YOUR website!

Hi,

the width of a rectangle is 2 meters less than the length'x', the area is 48m^2
A =
x^2 - 2x - 48 = 0
(x-8)(x+6) = 0, x = 8 (throwing out negative solution for unit measure
Rectangle is 8m by 6m (x-2m)

Question 815472: what is the length and breath of a rectangle if the diagonal is 72?

You can put this solution on YOUR website!
what is the length and breath [sic] of a rectangle if the diagonal is 72?
-------------

Question 815325: The rectangle has a area of 60 square feet write and solve an equation to find the value of X
You can put this solution on YOUR website!
The rectangle has a area of 60 square feet write and solve an equation to find the value of X
-----------
How is X related to the rectangle?

Question 815340: I have a rectangle with an area of 200cm2
I make the length 20% longer and the width 20% shorter
What is the new area?

You can put this solution on YOUR website!
I have a rectangle with an area of 200cm2
I make the length 20% longer and the width 20% shorter
What is the new area?
-------
Area = L*W = 200
New area = 0.8L*1.2W = 0.96*200 = 192

Question 814972: What are the dimension's ( L&H) of a rectangle who's diagonal is 65" (inches). ?
Found 2 solutions by FightinBlueHens, solver91311:
You can put this solution on YOUR website!
To find the answer to this question, you need to factor the number 65. (Really any two numbers that can be multiplied to get 65 will work, but we will use just whole numbers greater than 0).
The factors of 65 are 65 and 1, and 5 and 13. So either one of those 2 sets will work.

You can put this solution on YOUR website!

There is no way to tell. If you know one of the dimensions and the diagonal, you can find the other, or if you know some relationship between the dimensions, such as the length is some number of inches greater than the width or that the length and the width are in some specified proportion, then you would be able to figure it out. But all you can say for certain with the given information is that each of the dimensions satisfies the inequality

John

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

Question 814973: What is the perimeter of a rectangle with the dimensions of length v+3 and a width of 5
You can put this solution on YOUR website!

Hi,
rectangle with the dimensions of length v+3 and a width of 5

units

Question 814819: Find the perimeter of the rectangle
whose length is 40cm and a
diagonal is 41cm.

You can put this solution on YOUR website!
Let y = size of unknown side.
, because the diagonal is the hypotenuse of the triangle with the legs, 40 and y.

which is simplifiable as
--------- Do you recognize why?

Solved for y is the main missing piece to finding the answer to the actual question, which I now leave for you to finish.

Question 814820: The length of a rectangle is 6 ft less than twice the width. The area of the rectangle is 56 ft^2. Find the width of the rectangle.
You can put this solution on YOUR website!
x for length, y for width.
and .
Do you know what to do next?

Question 814789: I need to write a polynominal that describes the gray area of a rectangle.
Gray area is L= 14y-5, W=6y. There is a white rectangle inside the gray one L=3y + 5, W= 3y.

You can put this solution on YOUR website!
((14y-5)*(6y))-
((3y + 5)*(3y))
75y^2-45 y

Question 814746: the perimeter of a rectangle is 3 1/12. the width of the rectangle is 2/3. calculate the area of the rectangle.
You can put this solution on YOUR website!

Hi,
the perimeter of a rectangle is 3 1/12. the width of the rectangle is 2/3.
calculate the area of the rectangle.

2L = L = 21/24
A =

Question 814569: The length of a rectangle is 13 centimeters less than three times its width. Its area is 56 square centimeters. Find the dimensions of the rectangle
You can put this solution on YOUR website!

Hi,
The length of a rectangle is 13 centimeters less than three times its width.
Let x represent the width and (3x-13) the length

Question states***Its area is 56 square centimeters.
A =
Solving for x
3x^2 - 13x - 56 =0

x = 7 0r x = -16/6 (tossing out negative solution for unit measure)
Width is 7cm and length is 8cm (3x-13)

Question 814576: the length of a rectangle is 4 meters and its area is 12 square meters. what will be the diagonal of that rectangle.
You can put this solution on YOUR website!

Hi,
the length of a rectangle is 4 meters and its area is 12 square meters

A =
A = , w = 3m
Diagonal =

Question 814513: the area of a rectangle is 99 yd^2, and the length of the rectangle is 7 yd more than twice the width. what are the dimensions of the rectangle?
You can put this solution on YOUR website!
Lw = 99 sq.yd
L = 2w + 7
---
Lw = 99
(2w + 7)w = 99
2ww + 7w = 99
2ww + 7w - 99 = 0
---
the above quadratic equation is in standard form, with a=2, b=7, and c=-99
---
to solve the quadratic equation, plug this:
2 7 -99
---
the roots of the quadratic are:
-9
5.5
---
the negative root doesn't make sense as a length, so use the positive root:
---
w = 5.5
L = 18
---
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Question 814528: The length of a rectangle is 7 more than the width and the area is 98 sqft. what is the length and width of the rectangle?
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L = w + 7
Lw = 98
---
Lw = 98
(w + 7)w = 98
ww + 7w = 98
ww + 7w - 98 = 0
---
the above quadratic equation is in standard form, with a=1, b=7, and c=-98
---
to solve the quadratic equation, plug this:
1 7 -98
---
the roots of the quadratic are:
7
-14
---
the negative root doesn't make sense as a length, so use the positive root:
---
w = 7 feet
L = 14 feet
---
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Question 814330: the perimeter of a rectangle lot is 350ft. the length of the lot is 10ft. more than twice the width. find the deminsion of the lot?
Found 2 solutions by ewatrrr, TimothyLamb:
You can put this solution on YOUR website!

Hi,
P = 350ft
the length of the lot is 10ft more than twice the width
Let x and (2x+10) represent the width and length

2(2x+10) + 2x = 350ft
6x = 330ft
x = 55ft, the width. The length is 120ft (2x+10)

You can put this solution on YOUR website!
2L + 2w = 350
L = 2w + 10
---
2L + 2w = 350
2(2w + 10) + 2w = 350
4w + 20 + 2w = 350
6w = 330
---
w = 55
L = 2w + 10
L = 110 + 10
L = 120
---
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Question 814212: The bottom of a rectangular swimming pool has an area of 570 square meters. Its perimeter is 98 meters. What are the dimensions of the pool?
You can put this solution on YOUR website!
The emphasis is on the rectangular bottom of the pool. Depth is not relevant.
w for width, L for length.
wL is the area, so square meters.
Perimeter is meters.
Two equations in two unknown variables. Solve for one variable and substitute into the other equation and get the value for one variable...

as a start,
;

.
Can you continue this?

Question 814138: the length of the poster is 3.5 feet and the perimeter of the poster is 11.2 feet. what is the width of the poster? what is the area of the poster?
You can put this solution on YOUR website!
L = 3.5
2L + 2w = 11.2
---
2L + 2w = 11.2
2(3.5) + 2w = 11.2
7 + 2w = 11.2
2w = 4.2
---
w = 2.1 ft
L = 3.5 ft
a = Lw = 7.35 sq.ft.
---
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Question 813892: Imagine that there are 17 people running for 3 committee position in the city council with no returning incumbents. If order does not make a difference in their selection, how many total 3-member committees could be formed?

Question 813891: Find the length of the diagonal of a rectangle with a width of 70 inches and length of 168 inches?
You can put this solution on YOUR website!

Hi,
Find the length of the diagonal of a rectangle with a width of 70 inches
and length of 168 inches?
Diagonal =

Question 813791: A rectangle has a length that is 2 less than 3 times the width, if the area of this rectangle is 16, Find the dimensions and the perimeter

You can put this solution on YOUR website!
L = 3w - 2
a = Lw = 16
---
Lw = 16
(3w - 2)w = 16
3ww - 2w = 16
3ww - 2w - 16 = 0
---
the above quadratic equation is in standard form, with a=3, b=-2, and c=-16
---
to solve the quadratic equation, plug this:
3 -2 -16
---
the quadratic equation has two real roots:
root 1: 2.66666667 = 2 + 2/3 = 8/3
root 2: -2
---
the negative root doesn't make sense for a length, so use the positive root:
w = 8/3
L = 3w - 2
L = 3(8/3) - 2
L = 8 - 2
L = 6
---
p = 2L + 2w
p = 2(6) + 2(8/3)
p = 12 + (16/3)
p = (36/3) + (16/3)
p = 52/3
p = 17.333333 = 17 + 1/3
---
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Question 812950: The length of a rectangle is 5 inches more than the width. The perimeter is 38 inches. Find the length and width.