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SAT Math : How to find the perimeter of a rectangle

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Example Question #1 : Rectangles

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:

10(x + 1)

6x² + 5

5x + 10

6x² + 10x

5x + 5

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 #1 : How To Find The Perimeter Of A Rectangle

Find the perimeter of a rectangle with width 7 and length 9.

Possible Answers:

$\frac{63}{2}$

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle.

Substitute in the width of seven and the length of nine.

Thus,

P=2(w+l)=2*(7+9)=2*16=32

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Example Question #2 : How To Find The Perimeter Of A Rectangle

Find the perimeter of a rectangle whose side lengths are 1 and 2.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter of a rectangle. Thus,

P=2(w+l)=2*(1+2)=2*3=6

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Example Question #2 : How To Find The Perimeter Of A Rectangle

Find the perimeter of a rectangle with width 6 and length 9.

Possible Answers:

Correct answer:

Explanation:

To solve, simply use the formula for the perimeter.

P=2(w+l)

P=2*(6+9)=2*15=30

Another way to solve this problem is to add up all of the sides. Remember that even though only two values are given, a rectangle has 4 sides. Thus,

P=6+6+9+9=30

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Example Question #4 : How To Find The Perimeter Of A Rectangle

You have a poster of one of your favorite bands that you are planning on putting up in your dorm room. If the poster is 3 feet tall by 1.5 feet wide, what is the perimeter of the poster?

Possible Answers:

9.5ft

9ft

4.5ft^2

12ft

Correct answer:

9ft

Explanation:

You have a poster of one of your favorite bands that you are planning on putting up in your dorm room. If the poster is 3 feet tall by 1.5 feet wide, what is the perimeter of the poster?

Perimeter of a rectangle is found via:

P=2l+2w=2(3ft)+2(1.5ft)=6ft+3ft=9ft

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Example Question #3 : How To Find The Perimeter Of A Rectangle

Three of the vertices of a rectangle on the coordinate plane are located at the origin, (10, 0) , and (0, 7) . Give the perimeter of the rectangle.

Possible Answers:

Correct answer:

Explanation:

The rectangle in question is below:

Rectangle 3

The lengths of the rectangle is 10, the distance from the origin to (10,0) ; its width is 7, the distance from the origin to (0, 7) . The perimeter of a rectangle is equal to twice the sum of its length and width, so calculate:

$P= 2 (10+ 7 ) = 2 \times 17 = 34$ .

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Example Question #3 : How To Find The Perimeter Of A Rectangle

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:

$18\: \mbox{meters}$

$24\: \mbox{meters}$

$54\: \mbox{meters}$

$40\: \mbox{meters}$

$36\: \mbox{meters}$

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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SAT Math : How to find the perimeter of a rectangle

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Rectangles

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

Example Question #2 : How To Find The Perimeter Of A Rectangle

Example Question #2 : How To Find The Perimeter Of A Rectangle

Example Question #4 : How To Find The Perimeter Of A Rectangle

Example Question #3 : How To Find The Perimeter Of A Rectangle

Example Question #3 : How To Find The Perimeter Of A Rectangle

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