Pre-Algebra : Perimeter of a Rectangle or Square

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

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Example Question #1 : Perimeter Of A Rectangle Or Square

Michelle wants to put a fence up around her garden, which is 10 ft. long and 15 ft. wide. How long will her fence be? 

Possible Answers:

Correct answer:

Explanation:

Since the perimeter marks out the distance around a shape, you can imagine yourself walking around a shape to find the perimeter. For a rectangle, you would walk the same length twice (once on each side) and the same width twice (once on each side). That's why you multiply both the length and the width by 2. 

To find the perimeter, use the following formula:

 

Step 1: insert length and width into the formula

Step 2: solve

Example Question #2 : 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:

Correct answer:

Explanation:

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

Using the values given to us in the problem:

Thus, the perimeter is 98 yards.

Example Question #3 : 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:

Correct answer:

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.

Example Question #4 : 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:

Correct answer:

Explanation:

The correct answer is 

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.

Example Question #5 : Perimeter Of A Rectangle Or Square

Sarah has a purple square rug in the middle of her bedroom. The area of rug is . What is the length of each side of rug?

Possible Answers:

Correct answer:

Explanation:

The correct answer to the question is .

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 .

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

Therefore,  is by itself on the left side of the equation. We know that .

In this equation, . Therefore, the length of a side of Sarah's rug is .

Example Question #6 : Perimeter Of A Rectangle Or Square

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

Possible Answers:

Correct answer:

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.

Example Question #1 : Perimeter Of A Rectangle Or Square

The area of a square is  Find the perimeter of the square.

Possible Answers:

Correct answer:

Explanation:

The formula for finding the area of a square is  because each side is the same length. We are given that , so we can solve for s and get 

The formula for the perimeter is , but in the case of a square, , so the perimeter of a square is .

Example Question #2 : 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  section of fencing costs , and your garden is going to have a length of  and a width of , how much will you spend on fencing to completely enclose the garden?

Possible Answers:

Correct answer:

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:

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

 sections of fencing

Finally, we multiply this by the price per section.

 

Example Question #3 : 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:

The answer is not present.

Correct answer:

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?

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.

Example Question #4 : Perimeter Of A Rectangle Or Square

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

Possible Answers:

Correct answer:

Explanation:

Write the formula to find the perimeter of a square.

Substitute the side length.

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