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PSAT Math : How to find the perimeter of a rectangle

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Example Questions

Example Question #1 : How To Find The Perimeter Of A Rectangle

A rectangle has a width of 2x. If the length is five more than 150% of the width, what is the perimeter of the rectangle?

Possible Answers:

5x + 5

6x² + 5

10(x + 1)

5x + 10

6x² + 10x

Correct answer:

10(x + 1)

Explanation:

Given that w = 2x and l = 1.5w + 5, a substitution will show that l = 1.5(2x) + 5 = 3x + 5.

P = 2w + 2l = 2(2x) + 2(3x + 5) = 4x + 6x + 10 = 10x + 10 = 10(x + 1)

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Example Question #11 : Rectangles

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a rectangular garden (in green) surrounded by a dirt path (in orange). The dirt path is seven feet wide throughout. Which of the following polynomials gives the perimeter of the garden in feet?

Possible Answers:

$2x^{2}-42x +196$

6x - 28

6x-14

$2x^{2}-21x + 49$

6x - 56

Correct answer:

6x - 56

Explanation:

The length of the garden, in feet, is $2 \times 7 = 14$ feet less than that of the entire lot, or

L = 2x-14 ;

The width of the garden, in feet, is $2 \times 7 = 14$ less than that of the entire lot, or

W = x-14 .

The perimeter, in feet, is twice the sum of the two:

P = 2 (L + W)

= 2 (2x-14 + x - 14 )= 2 (3x-28) = 6x - 56

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Example Question #11 : Rectangles

Garden

Note: Figure NOT drawn to scale

Refer to the above figure, which shows a square garden (in green) surrounded by a dirt path (in orange) eight feet wide throughout. What is the perimeter of the garden?

Possible Answers:

$236 \textup{ ft}$

$134 \textup{ ft}$

$284\textup{ ft}$

$268 \textup{ ft}$

$118 \textup{ ft}$

Correct answer:

$236 \textup{ ft}$

Explanation:

The inner square, which represents the garden, has sidelength $(75 - 2\times 8) = 59$ feet, so its perimeter is four times this:

$P = 4 \times 59 = 236$ feet.

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Example Question #1 : How To Find The Perimeter Of A Rectangle

Farmer Dave has a rectangular field that is 50 yards wide and 40 yards long. He wants to enclose the field with a wire fence. How much wire does Farmer Dave need?

Possible Answers:

170 yards

180 yards

210 yards

200 yards

160 yards

Correct answer:

180 yards

Explanation:

To solve this problem, find the perimeter of the rectangle. There are two sides that each measure 50 yards and two sides that each measure 40 yards. Together these four sides measure 180 yards.

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Example Question #1 : Rectangles

A rectangular garden has an area of $80\: \mbox{m^2}$ . Its length is meters longer than its width. How much fencing is needed to enclose the garden?

Possible Answers:

$40\: \mbox{meters}$

$24\: \mbox{meters}$

$18\: \mbox{meters}$

$54\: \mbox{meters}$

$36\: \mbox{meters}$

Correct answer:

$36\: \mbox{meters}$

Explanation:

We define the variables as $w = \mbox{width}$ and $l = \mbox{length} = w + 2$ .

We substitute these values into the equation for the area of a rectangle and get $A_{\mbox{rectangle} }= wl = w(w + 2) = 80$ .

w^2 +2w-80=0

(w - 8)(w + 10) = 0

w = 8 or w = -10

Lengths cannot be negative, so the only correct answer is w = 8 . If w = 8 , then l = 10 .

Therefore, $\mbox{perimeter }= 2w + 2l = 16 + 20 = 36\:\mbox{m}$ .

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PSAT Math : How to find the perimeter of a rectangle

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 : How To Find The Perimeter Of A Rectangle

Example Question #11 : Rectangles

Example Question #11 : Rectangles

Example Question #1 : How To Find The Perimeter Of A Rectangle

Example Question #1 : Rectangles

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