GMAT Math : Calculating the length of the side of a rectangle

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Example Question #361 : Problem Solving Questions

The area of a rectangle is 85; its length is x - 17 . What is its width?

Possible Answers:

$51 - \frac{1}{2}x$

$\frac{85}{x-17 }$

$\frac{68}{x }$

102-x

$\frac{5}{x }$

Correct answer:

$\frac{85}{x-17 }$

Explanation:

The product of the length and the width of a rectangle is its area, so divide area by length to get width. This is simply $\frac{85}{x-17 }$ .

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Example Question #1 : Calculating The Length Of The Side Of A Rectangle

The perimeter of a rectangle is ; its width is 4t -26 . Which of the following expressions is equal to the length of the rectangle?

Possible Answers:

71-4t

116-4t

71+4t

$\frac{45}{2t-13}$

$\frac{45}{2t+13}$

Correct answer:

71-4t

Explanation:

Substitute P = 90, W = 4t-26 and solve for :

2 L + 2W = P

2 L + 2 (4t-26) = 90

2 L + 8t-52 = 90

2 L + 8t-52 + 52 - 8t= 90 + 52 - 8t

2 L =142 - 8t

$2 L \div 2=\left (142 - 8t \right ) \div 2$

L =71-4t

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Example Question #1 : Calculating The Length Of The Side Of A Rectangle

Rectangle A and Rectangle B have the same area. Rectangle A has length 80% that of Rectangle B, and its width is 120 centimeters. What is the width of Rectangle B?

Possible Answers:

$140 \textrm{ cm}$

Not enough information is given to answer the question.

$1 \textrm{ m}$

$96 \textrm{ cm}$

$144 \textrm{ cm}$

Correct answer:

$96 \textrm{ cm}$

Explanation:

Let and be the length and width of Rectangle B.

Then the width of Rectangle A is 80% of , or 0.8W . Its length is 120.

The area shared by the two can be expressed as both and $0.8W \cdot 120 = 96W$ . We can set the two equal to each other and calculate :

LW =96W , or L = 96 .

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Example Question #4 : Calculating The Length Of The Side Of A Rectangle

Craig is building a fence around his rectangular back yard. He knows that the yard is feet longer than twice the width. What is the width of the yard if Craig needs 160 feet of fencing to completely enclose the yard?

Possible Answers:

45ft

35ft

25ft

15ft

55ft

Correct answer:

25ft

Explanation:

The length is 5 more twice the width. Let y be the length of the yard and w the width.

y=2w+5

The perimeter of the yard is 160, so we can write:

2(y+w)=160

2(2w+5+w)=160

10+6w=160

w=25

The yard is 25 feet wide and 55 feet long.

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Example Question #5 : Calculating The Length Of The Side Of A Rectangle

A rectangle has an area of . If the width of the rectangle is , what is its length?

Possible Answers:

Correct answer:

Explanation:

Using the formula for the area of a rectangle, we can solve for the unknown length. We are given the area and the width, so we can solve for the length as follows:

A=LW

36=L(4)

$L=\frac{36}{4}=9$

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Example Question #6 : Calculating The Length Of The Side Of A Rectangle

The length of a rectangle is twice its width. If the rectangle's area is $288 \ in^2$ , what is its length?

Possible Answers:

$6 \ in$

$12 \ in$

$24 \ in$

$14 \ in$

Correct answer:

$24 \ in$

Explanation:

We're told the length is twice the width so l=2w

$A=l \times w=(2w)(w)$

288=2w^2

144=w^2

12=w

Remember, we're being asked for the length, not the width so:

$l=2w=2(12)=24 \ in$

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Example Question #7 : Calculating The Length Of The Side Of A Rectangle

A rectangle with a perimeter of has a width times that of its length. Find its length.

Possible Answers:

10.8

21.6

5.4

Correct answer:

5.4

Explanation:

The perimeter of a rectangle is found by 2l + 2w . Since we are told w=4l , we can substitute this into our equation and solve for the length.

54 = 2l + 2(4l)

54 = 10l

l = 5.4

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Example Question #8 : Calculating The Length Of The Side Of A Rectangle

The perimeter of a rectange equals $\textup{24in.}$ The length of the rectange equals four less than three times the width. What are the measurements of the length (l) and (w) of this rectangle?

Possible Answers:

$l=6\textup{in, }w=3\textup{in}$

$l=\textup{6in, }w=2\textup{in}$

$l=10\textup{in, }w=5\textup{in}$

$w=\textup{8in, }l=\textup{4in}$

$l=8\textup{in, }w=4\textup{in}$

Correct answer:

$l=8\textup{in, }w=4\textup{in}$

Explanation:

The perimeter of a rectangle can be found by the following formula: P=2l+2w. Let's substitute our values from the problem statement:

24in = 2l+2w -> 12in=l+w .

We also know from the second line that l=3w-4. Let's substitute that back into the perimeter equation, and solve for width. Then, we plug that back into the other eqution to get the answer for length.

12in=l+w=3w-4+w=4w-4.

16w=4w ->w=4.

$12in=l+w = l+4\textup{in} ->l=8\textup{in.}$

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GMAT Math : Calculating the length of the side of a rectangle

Study concepts, example questions & explanations for GMAT Math

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Example Questions

Example Question #361 : Problem Solving Questions

Example Question #1 : Calculating The Length Of The Side Of A Rectangle

Example Question #1 : Calculating The Length Of The Side Of A Rectangle

Example Question #4 : Calculating The Length Of The Side Of A Rectangle

Example Question #5 : Calculating The Length Of The Side Of A Rectangle

Example Question #6 : Calculating The Length Of The Side Of A Rectangle

Example Question #7 : Calculating The Length Of The Side Of A Rectangle

Example Question #8 : Calculating The Length Of The Side Of A Rectangle

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