# Questions on Geometry: Rectangles answered by real tutors!

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Question 994709: The length of a rectangle exceeds its width by 5 ft if the area of the rectangle is 176 square ft what are its dimensions.
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Find a pair of factors of 176 that differ by 5.

Question 994273: Some men pay 15p each for the hire of boat.
If there had been 2 more, they would pay 10p
each.How many men were there and cost to
hire boat.

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Some men pay 15p each for the hire of boat. If there had been 2 more, they would pay 10p each.How many men were there and cost to hire boat.
Number of men:
Cost to hire boat:



Question 994251: a local building code requires that all factories must be surrounded by a lawn. the width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. what must be the width of a lawn surrounding a rectangular that measures 120m by 80m?
Found 2 solutions by MathTherapy, josgarithmetic:
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a local building code requires that all factories must be surrounded by a lawn. the width of the lawn must be uniform and the area of the lawn must be equal to the area of the factory. what must be the width of a lawn surrounding a rectangular that measures 120m by 80m?
Width of lawn:  m



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Factory area, wL
Combined Factory & Lawn area, (w+2u)(L+2u)
Lawn area requirement,

Simplify that equation and solve for u.

Substitute whenever you are ready, but solve for u. Formula for general solution of quadratic equation can be used.

---
The PLUS form is needed in the formula for quadratic equation because we must have a positive value for u. w and L are both positive, but they are used as SUBTRACTED in the numerator of the formula of quadratic equation solution.

Most of the time, students would want to substitute the given values just after finding the quadratic equation in the green rectangular outline shown (IF they are starting the problem solution and analysis in symbolic form as done in this example).

Question 994258: a matte uniform width is to be placed around a painting so that the area of the matted surface is twice the area of the picture. If the outside of the matte are 40cm and 60cm, find the width of the matte.
i have the answer to the question i just dont know how to show my work doing it.

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Let the width of the matte be cm.
the outside dimensions of the matte are by cm
the length of the picture will be ... ( cm on each side, so )
the width of the picture will be
.
the area of the
the area of the
.
the area of the
.
=>

or
satisfies the equation, so the width of matte is

Question 994249: a playground which measures 60m by 40m is to be doubled in area by extending each side an equal amount. how much should each side be extended?

Question 994173: The length of a rectangle is 4in. Greater than its width. The perimeter of the rectangle is 24in. Find the dimensions of the rectangle.
W=width l=length
I know that to find the length it's 4+w(2)
I know that the width would be 2w
I just need help checking and I'm wondering if I'm missing anything

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.
W=width; L=length=W+4
.
P=2(L+W)
24in=2((W+4)+W)
12in=2W+4
8in=2W
4in=W
ANSWER 1: The width is 4 inches.
.
L=W+4
L=4+4=8
ANSWER 2: The length is 8 inches.
.
CHECK:
.
P=2(L+W)
24in=2(8in+4in)
24in=2(12in)
24in=24in

Question 994083: The length of a rectangle is 4 times its width. If the perimeter of the rectangle is 70 ft., find the area.
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and

Solve for then calculate

John

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

Question 993826: 18. Suppose that the length of a certain rectangle is times its width, and the area of that same rectangle is 160 square centimeters. Find the length and width of the rectangle. Answer: 20 centimeters and 8 centimeters

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the length of a certain rectangle is HOW MANY TIMES times its width??

Question 993773: A rectangle has a perimeter of 117.4 whose length is 8.7 more then the width. Find the length and the width?
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2x+2(x+8.7)=117.4
2x+2x+17.4=117.4
4x=117.4-17.4
x=100/4
x=25
x+8.7=33.7

Question 993675: A rectangle has a length of 12 inches more than three times its height. If the perimeter of a rectangle is 400 inches, find its dimensions.
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Here
L = 12 + 3H
P = 2L + 2H = 400
Substitute for L in the second equation and get
2(12 + 3H) + 2H = 400
24 + 6H + 2H = 400
8H + 24 = 400
8H = 376
H = 47
L = 12 + 3(47) = 153

Question 993576: The length of a rectangle is 17 meters less than twice the width. The perimeter of the rectangle is 203 meters. Find the dimensions.
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Hi there,
Make the width = 'x'
Length = 2x - 17
Perimeter = 2 x Width + 2 x Length
203 = 2(x) + 2(2x - 17)
203 = 2x + 4x - 34
collect like terms.
2x + 4x = 203 + 34
6x = 237
x = 237/6
x = 39.5 meters
Width = 39.5 meters
Length = 62 meters
Hope this helps :-)

Question 993551: The perimeter of the rectangle is 70cm. The length is 4x+3) and the width is (2x+8)find the area

Found 2 solutions by addingup, josgarithmetic:
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Let's work with what we know:
The perimeter is:
2L+2W= 70 Now using the values provided by the problem:
2(4x+3)+2(2x+8)= 70 Let's multiply on the left
8x+6+4x+16= 70 Add on the left
12x+22= 70 Subtract 22 on both sides
12x= 48 Divide both sides by 12
x= 4 OK, now we know the value of x, we can find the length and width:
4(4)+3= 16+3= 19 is our length
2(4)+8= 16 is our width. Check, perimeter is:
2(16)+2(19)= 70
32+38= 70
70=70 We've got the right answer. Now for the area:
A= L*W= 19*16= 304 is your area.
And there you have it.

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Solve for x.

Now evaluate .

Question 993510: a pool has a perimeter of 82 m, the length equals 5m more than twice the width, find length and width.
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P=2L+2W
82=2L+2W
41=L+W, dividing by 2
L=2W+5
2W+5+W=41
3W=36
W=12 m
L=29 m
Twice their sum is 82 m.

Question 993467: The dimensions of a shape with an area of 10 and perimeter of 22
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A=LW
10=LW
10/L=W
.
P=2(L+W)
22=2(L+W)
11=L+W
11=L+10/L

L-1=0 OR L-10=0
L=1 OR L=10
.
If length=1, width=10/1=10
If length=10, width=10/10=1
.
CHECK:
A=LW
10=(10)(1)
10=10
.
P=2(L+W)
22=2(10+1)
22=2(11)
22=22

Question 993268: the perimeter of a rectangle is 24cm. if the length is triple the width, find the area of the rectangle.
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W=width; L=length=3W
.
P=2(L+W)
24cm=2(3W+W)
12cm=4W
3cm=W
L=3W=3(3cm)=9cm
.
Area=LW=(9cm)(3cm)=27cm^2
.
ANSWER: The area of the rectangle is 27 square centimeters.

Question 993260: a rectangle is 4 feet longer than its width. if the area of the rectangle is 369 sq feet what is its width in feet?
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a rectangle is 4 feet longer than its width. if the area of the rectangle is 369 sq feet what is its width in feet?
let x=width of rectangle
x+4=length of rectangle
length*width=area
x(x+4)=369
x^2+4x-369=0
solve for x by quadratic formula:

a=1, b=4, c=-369
ans: x=17.31
width=17.31 ft
length=21.31 ft

Question 993257: The difference between the length and width of a rectangular garden is 5 meters. The perimeter of the garden is 100 meters. Find the length and width of the garden.
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L-W= 5, therefore L= W+5
2L+2W= 100 Substitute:
2(W+5)+2W= 100
2W+10+2W= 100 Add the W and subtract 10 from both sides
4W= 90 Divide both sides by 4
W= 22.5 And the problem says the length is 5 more:
L= 27.5
Let's proof this:
2L+2W= 100
2(27.5)+2(22.5)= 100
55+45= 100
100= 100 We have the correct answer.

Question 992493: The ratio of the length of a rectangle to its width is 3/2 and the width is 24 centimeters, what is the rectangle’s perimeter?
Found 2 solutions by MathTherapy, Timnewman:
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The ratio of the length of a rectangle to its width is 3/2 and the width is 24 centimeters, what is the rectangle’s perimeter?
Perimeter:  cm



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let L=lenght,
w=width
Ratio of L to w=3:2
If w=24cm,
Then,
3/2=L/24
Multiply out,
2L=72
L=36cm
Perimeter P=2(L+w)
p=2(24+72)
p=2(96)
p=192cm
The perimeter is 192cm
HOPE THIS HELPS?
::TIMNEWMAN::

Question 992424: Find the perimeter of the rectangle with length of 3x, width of 2x-1 and area of 45m^2
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Hi dear,
If lenght L=3x----(1)
and width w=2x-1--(2)
Annd,
L*w=45----(3)
Put equ 1 and 2 in 3
3x(2x-1)=45
6x²-3x-45=0
Solve the quadratic equation as follows
 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=1089 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3, -2.5. Here's your graph:

Since x=3 or -2.5
L=3(3)=9m
Or
L=3(-2.5)=-7.5m
Now,w=2(3)-1=5m
Or,
w=2(-2.5)-1=-6
Ingnore those once having the nagative sign
Then,
Perimeter p=2(L+w)
p=2(9+5)m
p=28m
The perimeter of the figure is 28meters.
HOPE THIS HELPS?

Question 992403: What are the length and width of a rectangular traffic sign if the length exceeds the width by 12 inches and the perimeter is 176 inches
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What are the length and width of a rectangular traffic sign if the length exceeds the width by 12 inches and the perimeter is 176 inches.
-----
width: x
length: x+12
--------
P = 2(length + width)
176 = 2(x+12+x)
----
88 = 2x+12
---
2x = 76
x = 38 (width)
x+12 = 50 (length)
----------------
Cheers,
Stan H.
--------

Question 992316: A rectangle has an area of 36 square metres. In exact form, what is the perimeter of the rectangle?
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.
There is no enough data.
Do you understand it?

Question 992123: find the dimensions of a rectangle with a perimeter of 64 meters if its length is 4 meters less than twice the width.
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.
W=width; L=length=2W-4m
.
P=2(L+W)
64m=2(2W-4m+W)
32m=3W-4m
36m=3W
12m=W . ANSWER 1: The width is 12 meters.
.
L=2W-4m=2(12m)-4m=24m-4m=20m
ANSWER 2: The length is 20 meters.
.
CHECK:
P=2(L+W)
64m=2(20m+12m)
64m=2(32m)
64m=64m

Question 992189: The sum of two numbers is 130 and their difference is 22

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Same problem, different numbers.
-----
The sum of two numbers is 12. The difference of the same two numbers is -4. Find the numbers.
==========================
x + y = 12
x - y = -4

Question 992032: the area of a circle is 25 • pi. find the circumference.
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10*3.14=31.4

Question 992034: The width of a rectangle measures one half of the length. If the area is 72 square feet, then find the dimensions of the rectangle.
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.
W=width; L=length=2W
.
A=LW
72ft^2=2W(W)
72ft^2=2W^2
36ft^2=W^2
6ft=W
L=2W+2(6ft)=12ft
ANSWER: The rectangle is 12 feet x 6 feet.

Question 991997: the length of a rectangle is half the width. the area is 25 square meters. what is the perimeter?
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If the length is half of the width and the area is 25, then . Solve for , calculate the length, then use the width and the length in the perimeter formula.

John

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

Question 991778: The length of a rectangle is 5 more than 3 times its width. The perimeter of the rectangle is 58 inches. What is the length of the rectangle?

Question 991771: a rectangle has a base of x units. the perimeter is (6x+10). what is the area of a rectangle un terms of x
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a rectangle has a base of units,
the perimeter is

Area of a rectangle is calculated as follows:
...since and , we will have

Question 991734: The lengths of the sides of a rectangle are in the ratio 5 : 3. The perimeter is 32 cm. What are the dimensions?
A. (35)w+w=32
15 cm by 9 cm
B. 2(35)w+2w=32
10 cm by 6 cm
C. (35)w+w=32
20 cm by 12 cm
D. 2(35)w+2w=32
25 cm by 15 cm

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The lengths of the sides of a rectangle are in the ratio 5 : 3. The perimeter is 32 cm. What are the dimensions?
----
Let length = 5x, then width = 3x
-----
P = 2(L + W)
32 = 2(8x)
16 = 8x
x = 2
----
Length = 5x = 10 cm
Width = 3x = 6 cm
------------.
Cheers,
Stan H.
----------

Question 991449: the length of a rectangle is 4 centimeters more than twice its width.If the perimeter of the rectangle is 86 centimeters,find the dimensions of the rectangle.

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Hi there,
Make Width = 'x'
Length = 4 + 2x
Perimeter = 2 x Width + 2 x Length
86 = 2(x) + 2(4 + 2x)
86 = 2x + 8 + 4x
Collect like terms:
2x + 4x = 86 - 8
6x = 78
x = 13
Width = 13 cm
Length = 30 cm
Hope this helps :-)

Question 991448: The perimeter of a rectangular frame is 98cm. The length of the rectangle is 3 more than the width. What is the length and width of the rectangle?u

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Hi there,
Make the width = 'x'
Length = x + 3
Perimeter of a rectangle =
2 x Width + 2 x Length
98cm = 2(x) + 2(x + 3)
98cm = 2x + 2x + 6
Collect like terms:
2x + 2x = 98 - 6
4x = 92
x = 23
Width = 23 cm
Length = 26 cm
Hope this helps :-)

Question 991461: the length of a rectangle is 5 less than twice its width.The perimeter is 26 meters.Find the dimensions of the rectangle
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Hi there,
Make Width = 'x'
Length = 2x - 5
Perimeter of a rectangle =
2 x Width + 2 x Length
26m = 2(x) + 2(2x - 5)
26m = 2x + 4x -10
Collect like terms:
2x + 4x = 26 + 10
6x = 36m
x = 6m
Width = 6m
Length = 7m
Hope this helps :-)

Question 991454: the length of a rectangle is 3 inches more than its width.If the perimeter is 42 inches,find the dimensions of the rectangle
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.
W=width; L=length=W+3in
.
P=2(L+W)
42in=2(W+3in+W)
21in=2W+3in
18in=2W
9in=W
ANSWER 1: The width is 9 inches
L=W+3in=9in+3in=12 in
ANSWER 2: The length is 12 inches.
.
CHECK:
P+2(L+W)
42in=2(12in+9in)
42in=2(21in)
42in=42in

Question 991380: the perimeter of a rectangle is 176 cm. the length is equal to 3 times the width decreased by 4. Find the dimensions of the rectangle
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the perimeter of a rectangle is 176 cm.
2L + 2W = 176
simplify, divide by 2
L + W = 88
the length is equal to 3 times the width decreased by 4.
L = 3W
Find the dimensions of the rectangle
Replace L in the 1st simplified equation with 3W
3W + W = 88
4W = 88
W = 88/4
W = 22 is the width
then
3(22) = 66 cm is the length

Question 991316: The perimeter of a rectangle is
46 yards The area of the rectangle is
76 square yards Find the dimensions of the rectangle

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The perimeter of a rectangle is
46 yards
P = 2L + 2W = 46
L + W = 23
-----------------------
The area of the rectangle is
76 square yards Find the dimensions of the rectangle
---
Find a pair of factors of 76 with a sum of 23
eg,
1*76 NG
2*38 NG
etc

Question 991319: find the three dimensions of the perimeter, 8xy+2x+4y+2
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Makes no sense.

Question 991311: If a door has a length of 5feet and width of 7feet what's the area in square inches
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If a door has a length of 5feet and width of 7feet what's the area in square inches
========
Area = L*W
1 sq ft = 12*12 = 144 sq inches.
------------
Or
Area = 60 in * 84 in

Question 991151: The perimeter of the rectangle is 52m. The length is 6m more than the width. Label set up an equation, and solve for the width and length of the below rectangle.
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Hi there,
Make the width = 'x'
Length = x + 6
Perimeter = 2 x Width + 2 x Length
52 = 2(x) + 2(x + 6)
52 = 2x + 2x + 12
Collect like terms:
4x = 52 - 12
4x = 40
x = 10
Width = 10m
Length = 16m
Hope this helps :-)

Question 991269: in a trapezoid the smaller base is three more than the height the larger base is five less than three times the height in the area of the trapezoid is 45 cm² find in centimeters the height of the trapezoid
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h, height
b, bottom base

The third equation is the expressions used in the formula for area of a trapezoid. Solve for h, the only variable in that equation.

Question 991234: A rectangular lawn has an area of 280 square meters. Its perimeter is 68 meters. What are the dimensions of the lawn?
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A rectangular lawn has an area of 280 square meters. Its perimeter is 68 meters. What are the dimensions of the lawn
===================
Check for an integer solution first.
---
P = 2W + 2L = 68
W + L = 34
W*L = 280
---------------------------------
Find a pair of factors of 280 with a sum of 34
---
eg
1*280 NG
2*140 NG
etc

Question 991213: A rectangle has a perimeter of 130 centimeters. If the length of the rectangle is 4 times its width, find the dimensions of the rectangle.
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A rectangle has a perimeter of 130 centimeters. If the length of the rectangle is 4 times its width, find the dimensions of the rectangle.
---------------
width:: x
length:: 4x
----
perimeter = 2(length + width)
130 = 2(5x)
x = 13 (width)
4x = 52 (length)
---------
Cheers,
Stan H.
------

Question 991095: Find the perimeter for the figure. The length of a rectangle is half the width. The area is 25 square meters.
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Find the perimeter for the figure. The length of a rectangle is half the width. The area is 25 square meters.
---
width:: 2x
length:: x
-----
Area = 2x^2 = 25
x = 5/sqrt(2) or (5/2)sqrt(2)------ length
2x = 5sqrt(2)......... width
------------------------
Ans: Perimeter = 2[length + width]
---
P = 2[(7/2)sqrt(2)]
P = 7sqrt(2)
-----------------
Cheers,
stan H.
------