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Pre-Algebra : Perimeter

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #3 : Perimeter Of A Rectangle Or Square

Sarah has a purple square rug in the middle of her bedroom. The area of rug is $16\:in^2$ . What is the length of each side of rug?

Possible Answers:

$4\:in$

$2\:in$

$5\:in$

$8\:in$

$16\:in$

Correct answer:

$4\:in$

Explanation:

The correct answer to the question is $4\:in$ .

The formula for the perimeter of a square is times the length of a side. We know this because all sides of a square are equal to one another.

Our unknown number is the length of each side which we set to . In this scenario, we know that the equation is 4x = 16 .

In order to solve for , we divide each side of the equation by :

$\frac{4x}{4} = \frac{16}{4}$

x=4

Therefore, is by itself on the left side of the equation. We know that 16/4=4 .

In this equation, x = 4 . Therefore, the length of a side of Sarah's rug is $4\:in$ .

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Example Question #4 : Perimeter Of A Rectangle Or Square

If one side of a square is feet long, what is the perimeter of that square?

Possible Answers:

$20 \textup{ ft}$

$10 \textup{ ft}$

$25 \textup{ ft}$

$15 \textup{ ft}$

Correct answer:

$20 \textup{ ft}$

Explanation:

To find the preimeter of a square you add all the sides of the square together.

Since the question told us the length of a side of the square, and we know that all sides of a square are equal we can plug this number into the following equation.

P=s_1+s_2+s_3+s_4

5+5+5+5=20

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Example Question #6 : Perimeter Of A Rectangle Or Square

The area of a square is $64\textup{ in.}^{2}$ Find the perimeter of the square.

Possible Answers:

$32\textup{ in.}$

$512\textup{ in.}$

$16\textup{ in.}$

$4096\textup{ in.}$

$8\textup{ in.}$

Correct answer:

$32\textup{ in.}$

Explanation:

The formula for finding the area of a square is $A=s^{2}$ because each side is the same length. We are given that A=64 , so we can solve for s and get $s=8 \, in.$

The formula for the perimeter is 2L+2W , but in the case of a square, L=W=s , so the perimeter of a square is P=4s .

$P=4(8\, in.)=32\,in.$

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Example Question #4 : Perimeter Of A Rectangle Or Square

You are designing a rectangular garden for the backyard, and you need to purchase fencing to put around it. If each 10 ft section of fencing costs $\$20$ , and your garden is going to have a length of 35 ft and a width of 15 ft , how much will you spend on fencing to completely enclose the garden?

Possible Answers:

$\$150$

$\$100$

$\$200$

$\$700$

$\$350$

Correct answer:

$\$200$

Explanation:

First, we need to find the perimeter of the garden to detemine how many feet of fencing we have to buy. We find the perimeter (P) of the rectangular garden using the following equation:

P = 2L + 2W

$P = 2\left ( 35ft\right ) + 2\left ( 15ft\right )$

P = 100ft

Now, we need to figure out how many sections of fencing we need to buy.

$100ft \div 10ft = 10$ sections of fencing

Finally, we multiply this by the price per section.

$10 \times \$20 = \$200$

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Example Question #6 : Perimeter Of A Rectangle Or Square

The perimeter of a chicken pen is equal to 22ft. If the width of the pen is 5 feet, how many feet is the length of the pen?

Possible Answers:

L=12ft

L=10ft

L=6ft

The answer is not present.

L=5ft

Correct answer:

L=6ft

Explanation:

In order to solve this problem you need to either know the formula for the perimeter of a rectangle or recognize there are 4 sides and two pairs of equal sides.

The problem states that the perimeter is 22 feet and that the width of the pen is 5 feet. Since rectangles have two pairs of equal sides we now can account for 10 feet of the perimeter. The are two remaining sides we do not know. Can you make an equation to represent what we know?

22ft=10ft+2L

This says that the total perimeter (22ft) is to 10ft plus 2L (L is just a variable for length; we could just as easily have used x). Solve for L.

$22ft=10ft+2L\rightarrow 12ft=2L\rightarrow L=6ft$

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Example Question #5 : Perimeter Of A Rectangle Or Square

If the square has a length of x^2 , what is the perimeter of the square?

Possible Answers:

x^8

8x^2

4x^2

Correct answer:

4x^2

Explanation:

Write the formula to find the perimeter of a square.

A=4s

Substitute the side length.

A=4(x^2) = 4x^2

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Example Question #6 : Perimeter Of A Rectangle Or Square

Find the perimeter of a square with a length of $\frac{4}{7}$ .

Possible Answers:

$\frac{8}{7}$

$\frac{32}{7}$

$\frac{16}{7}$

$\frac{1}{7}$

$\frac{16}{11}$

Correct answer:

$\frac{16}{7}$

Explanation:

Write the formula to find the perimeter of a square.

P=4s

Substitute the side length.

$P=4\left(\frac{4}{7}\right) = \frac{16}{7}$

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Example Question #21 : Perimeter

If the diagonal of a square is $6\sqrt2$ , what is the perimeter?

Possible Answers:

$24\sqrt2$

$48\sqrt2$

Correct answer:

Explanation:

Write the formula to obtain the side given the diagonal for squares.

$s=\frac{d}{\sqrt2} = \frac{6\sqrt2}{\sqrt2} =6$

The perimeter of the square is four times the side.

The answer is .

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Example Question #22 : Perimeter

What is the perimeter of a square with a side length of x-2y ?

Possible Answers:

8x-y

8xy

-4xy

4x-y

4x-8y

Correct answer:

4x-8y

Explanation:

Write the formula to find the perimeter of a square.

P=4s

Substitute the side.

P=4(x-2y) = 4x-8y

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Example Question #13 : Perimeter Of A Rectangle Or Square

Find the perimeter of a square in feet if the side length is 8 inches.

Possible Answers:

384

$\frac{8}{3}$

Correct answer:

$\frac{8}{3}$

Explanation:

Convert the 8 inches to feet by dividing 12. There are 12 inches in a foot.

$8\textup{ inches }= \frac{8}{12} \textup{ foot} = \frac{2}{3}\textup{ foot}$

Write the formula for the perimeter of a square.

P=4s

Substitute the side.

$P=4 (\frac{2}{3}) = \frac{8}{3}$

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Pre-Algebra : Perimeter

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #3 : Perimeter Of A Rectangle Or Square

Example Question #4 : Perimeter Of A Rectangle Or Square

Example Question #6 : Perimeter Of A Rectangle Or Square

Example Question #4 : Perimeter Of A Rectangle Or Square

Example Question #6 : Perimeter Of A Rectangle Or Square

Example Question #5 : Perimeter Of A Rectangle Or Square

Example Question #6 : Perimeter Of A Rectangle Or Square

Example Question #21 : Perimeter

Example Question #22 : Perimeter

Example Question #13 : Perimeter Of A Rectangle Or Square

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