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SSAT Upper Level 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

The length and width of a rectangle are x + 16 and 2x-7 . Give its perimeter in terms of .

Possible Answers:

$2x^{2} -25x -112$

6x+18

$2x^{2} +25x -112$

6x+46

3x+9

Correct answer:

6x+18

Explanation:

A rectangle has perimeter P = 2L + 2W , the length and the width. Substitute L= x + 16 and W = 2x-7 in the perimeter formula, and simplify.

P = 2L + 2W

$= 2 \left ( x+16\right ) + 2 \left ( 2x-7\right )$

$= 2 \cdot x+2 \cdot 16 +2 \cdot 2x-2 \cdot 7$

= 2x+32 +4x-14

= 6x+18

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

A rectangle has length 30 inches and width 25 inches. Which of the following is true about its perimeter?

Possible Answers:

Its perimeter is between 9 and 10 feet.

Its perimeter is between 8 and 9 feet.

Its perimeter is between 5 and 6 feet.

Its perimeter is between 4 and 5 feet.

Its perimeter is between 10 and 11 feet.

Correct answer:

Its perimeter is between 9 and 10 feet.

Explanation:

In inches, the perimeter of the rectangle can be calculated by substituting L = 30, W = 25 in the following formula:

P = 2 (L + W)

$P = 2 (30 + 25) = 2\times 55 = 110$

The perimeter is 110 inches.

Now divide by 12 to convert to feet:

$110 \div 12 = 9 \textrm{ R }2$

This makes the perimeter 9 feet 2 inches, which is between 9 feet and 10 feet.

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

Perimeter of a rectangle is 36 inches. If the width of the rectangle is 3 inches less than its length, give the length and width of the rectangle.

Possible Answers:

L=10, W=7 inches

L=10.5, W=7.5 inches

L=12, W=9 inches

L=11, W=8 inches

L=11.5, W=8.5 inches

Correct answer:

L=10.5, W=7.5 inches

Explanation:

Let:

$Length=x\Rightarrow Width=x-3$

The perimeter of a rectangle is P=2L+2W , where is the length and is the width of the rectangle. The perimeter is known so we can set up an equation in terms of and solve it:

P=2L+2W=2(x)+2(x-3)=36

$\Rightarrow2x+2x-6=36$

$\Rightarrow 4x-6=36$

$\Rightarrow 4x=42$

$\Rightarrow x=10.5$

So we can get:

Length=x=10.5 inches

Width=x-3=10.5-3=7.5 inches

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

The length and width of a rectangle are t+1 and t-1 , respectively. Give its perimeter in terms of .

Possible Answers:

4t-4

2t+2

4t+4

2t-2

Correct answer:

Explanation:

The perimeter of a rectangle is P=2L+2W , where is the length and is the width of the rectangle. In order to find the perimeter we can substitute the L=t+1 and W=t-1 in the perimeter formula:

=2(t+1)+2(t-1)

=2t+2+2t-2

=4t

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

The length of a rectangle is 2x+4 and the width of this rectangle is meters shorter than its length. Give its perimeter in terms of .

Possible Answers:

8x+6

10x+8

8x+8

10x+6

8x+10

Correct answer:

8x+10

Explanation:

The length of the rectangle is known, so we can find the width in terms of :

Width=Length-3=(2x+4)-3=2x+1

The perimeter of a rectangle is P=2L+2W , where is the length and is the width of the rectangle.

In order to find the perimeter we can substitute the L=2x+4 and W=2x+1 in the perimeter formula:

P=2L+2W

=2(2x+4)+2(2x+1)

=4x+8+4x+2

=8x+10

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Example Question #5 : How To Find The Perimeter Of A Rectangle

A rectangle has a length of t^2 inches and a width of inches. Which of the following is true about the rectangle perimeter if t=5 ?

Possible Answers:

Its perimeter is less than 7 feet.

Its perimeter is between 7.2 and 7.4 feet.

Its perimeter is between 7 and 8 feet.

Its perimeter is between 8 and 9 feet.

Its perimeter is more than 8 feet.

Correct answer:

Its perimeter is between 7 and 8 feet.

Explanation:

Substitute t=5 to get and :

L=t^2=5^2=25

$W=5t=5\times 4=20$

The perimeter of a rectangle is P=2L+2W , where is the length and is the width of the rectangle. So we have:

$P=2L+2W=2\times 25+2\times20=50+40=90$ inches

Now we should divide the perimeter by 12 in order to convert to feet:

$Perimeter=90\div 12=7.5$ feet

So the perimeter is 7 feet and 6 inches, which is between 7 and 8 feet.

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

Which of these polygons has the same perimeter as a rectangle with length 55 inches and width 15 inches?

Possible Answers:

A regular octagon with sidelength two feet

A regular hexagon with sidelength two feet

A regular heptagon with sidelength two feet

The other answer choices are incorrect.

A regular pentagon with sidelength two feet

Correct answer:

The other answer choices are incorrect.

Explanation:

The perimeter of a rectangle is twice the sum of its length and its width; a rectangle with dimensions 55 inches and 15 inches has perimeter

2 (55+15) = 140 inches.

All of the polygons in the choices are regular - that is, all have congruent sides - and all have sidelength two feet, or 24 inches, so we divide 140 by 24 to determine how many sides such a polygon would need to have a perimeter equal to the rectangle. However,

$140 \div 24 = 5 \frac{5}{6}$ ,

so there cannot be a regular polygon with these characteristics. All of the choices fail, so the correct response is that none are correct.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : How to find the perimeter of a rectangle

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

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 #3 : How To Find The Perimeter Of A Rectangle

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

Example Question #5 : How To Find The Perimeter Of A Rectangle

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

All SSAT Upper Level Math Resources

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