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Pre-Algebra : Perimeter of a Rectangle or Square

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #1 : Perimeter Of A Rectangle Or Square

Susy's yard is 32 yards by 17 yards. What is the total perimeter of her yard?

Possible Answers:

$\small 544\ \textup{yards}$

$\small 49\ \textup{yards}$

$\small 108\ \textup{yards}$

$\small 98\ \textup{yards}$

Correct answer:

$\small 98\ \textup{yards}$

Explanation:

Recall, the perimeter of a rectangle = 2*length + 2*width

Using the values given to us in the problem:

$\small Perimeter = (2*34)+(2*17) = 64+34 = 98$

Thus, the perimeter is 98 yards.

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Example Question #2 : Perimeter Of A Rectangle Or Square

Sally has a rectangular garden that is surrounded by a 6ft-wide and 8ft-long fence. However, she wants to expand her garden so that it is twice as wide and twice as long. What is the new perimeter of her garden?

Possible Answers:

$50\ \textup{ft.}$

$56\ \textup{ft.}$

$46\ \textup{ft.}$

$48\ \textup{ft.}$

$28\ \textup{ft.}$

Correct answer:

$56\ \textup{ft.}$

Explanation:

We know the original garden is a 6ft by 8ft rectangle. sally wants to expand her garden so that the new rectangle is twice as long and twice as wide, so the new dimensions are 12ft by 16ft.

The perimeter of a rectangle with these dimensions is

12*2 +16*2 = 56.

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Example Question #3 : Perimeter Of A Rectangle Or Square

Choose the correct equation to solve for the perimeter of the rectangle.

Peter's backyard is a rectangle. Two sides of his lawn are feet long, and two sides of his lawn are feet long.

Possible Answers:

20 + 15 = 35

4(20) + 15 = 95

20 + 2(15) = 50

2(20) + 2(15) = 70

2(20) + 15 = 55

Correct answer:

2(20) + 2(15) = 70

Explanation:

The correct answer is 2(20) + 2(15) = 70

Rectangles have sets of equal sides. In this example, one set of these sides is feet long and one set is feet long.

Therefore, multiplying the length of each side by two then adding these together will produce the perimeter.

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Example Question #4 : 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:

$5\:in$

$4\:in$

$2\:in$

$8\:in$

$16\:in$

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 #3 : Perimeter Of A Rectangle Or Square

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

Possible Answers:

$15 \textup{ ft}$

$25 \textup{ ft}$

$10 \textup{ ft}$

$20 \textup{ ft}$

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 #1 : 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:

$\$700$

$\$350$

$\$150$

$\$200$

$\$100$

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 #7 : 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=6ft

L=5ft

The answer is not present.

L=12ft

L=10ft

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 #4 : Perimeter Of A Rectangle Or Square

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

Possible Answers:

8x^2

x^8

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 #5 : Perimeter Of A Rectangle Or Square

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

Possible Answers:

$\frac{1}{7}$

$\frac{8}{7}$

$\frac{32}{7}$

$\frac{16}{11}$

$\frac{16}{7}$

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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Pre-Algebra : Perimeter of a Rectangle or Square

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #1 : Perimeter Of A Rectangle Or Square

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Example Question #3 : Perimeter Of A Rectangle Or Square

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