Squares

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ISEE Middle Level Quantitative Reasoning › Squares

Questions 1 - 10
1

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.

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

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

4

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.

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

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.

8

The perimeter of a square is 56in. Find the length of one side.

Explanation

To find the perimeter of a square, we use this formula

where a is the length of one side. A square has 4 equal sides. That is why we multiply the length of one side by 4. To find the length of one side, we will solve for a.

Now, we know the perimeter of the square is 56in. So, we can substitute. We get

Therefore, the length of one side of the square is 14in.

9

Find the area of a square with a width of 12cm.

Explanation

To find the area of a square, we will use the following formula:

where l is the length and w is the width of the square.

Now, we know the width of the square is 12cm. Because it is a square, all sides are equal. Therefore, the length is also 12cm.

Knowing this, we will substitute into the formula. We get

10

Find the area of a square with a length of 11in.

Explanation

To find the area of a square, we will use the following formula:

where l is the length and w is the width of the square.

Now, we know the length of the square is 11in. Because it is a square, all sides are equal. Therefore, the width is also 11in.

Knowing this, we will substitute into the formula. We get

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