Squares

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ISEE Middle Level Quantitative Reasoning › Squares

Questions 1 - 10
1

What is the length of a rectangular room with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

2

What is the perimeter of a square with area 196 square inches?

It cannot be determined from the information given.

Explanation

A square with area 196 square inches has sidelength inches, and therefore has perimeter inches

3

Angela has a garden that she wants to put a fence around. How much fencing will she need if her garden is by

Explanation

The fence is going around the garden, so this is a perimeter problem.

4

David wants to put a fence around his backyard. How much fencing will he need if his backyard is by

Explanation

The fence is going around the backyard, so this is a perimeter problem.

5

What is the length of a rectangular room with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

6

What is the length of a rectangular room with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

7

Each side of a square is units long. Which is the greater quantity?

(A)

(B) The perimeter of the square

(A) and (B) are equal

(A) is greater

(B) is greater

It is impossible to determine which is greater from the information given

Explanation

The perimeter of a square is four times its side length:

Since the perimeter is equal to , (A) and (B) are equal.

8

What is the length of a yard with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

9

What is the length of a yard with a perimeter of and a width of

Explanation

We have the perimeter and the width, so we can plug those values into our equation and solve for our unknown.

Subtract from both sides

Divide by both sides

10

A square has an area of 36, and each side is equal to What is the value of ?

Explanation

Each side of a square is equal to the square root of the area. The square root of 36 is 6, so each side is 6. Thus, 3x (being a side of the square is equal to 6. This means that x is equal to 2 because 3 times 2 is 6.

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