### All ACT Math Resources

## Example Questions

### Example Question #850 : Plane Geometry

A square garden has an area of 64 square feet. If you add 3 feet to each side, what is the new perimeter of the garden?

**Possible Answers:**

121

20

25

44

32

**Correct answer:**

44

By finding the square root of the area of the garden, you find the length of one side, which is 8. We add 3 feet to this, giving us 11, then multiply this by 4 to get 44 feet for the perimeter.

### Example Question #6 : How To Find The Perimeter Of A Square

The area of the shaded region of a square is 18. What is the perimeter of the square?

**Possible Answers:**

28

24

20

36

**Correct answer:**

24

The area of the shaded region, which covers half of the square is 18 meaning that the total area of the square is 18 x 2, or 36. The area of a square is equal to the length of one side squared. Since the square root of 36 is 6, the length of 1 side is 6. The perimeter is the length of 1 side times 4 or 6 x 4.

### Example Question #1 : How To Find The Perimeter Of A Square

The area of a square is . If the square is enlarged by a factor of 2, what is the perimeter of the new square?

**Possible Answers:**

**Correct answer:**

The area of a square is given by so we know the side is 5 cm. Enlarging by a factor of two makes the new side 10 cm. The perimeter is given by , so the perimeter of the new square is 40 cm.

### Example Question #2 : How To Find The Perimeter Of A Square

The diagonal of a square has a length of 10 inches. What is the perimeter of the square in inches squared?

**Possible Answers:**

**Correct answer:**

Using the Pythagorean Theorem, we can find the edge of a side to be √50, by 2a^{2}=10^{2}. This can be reduced to 5√2. This can then be multiplied by 4 to find the perimeter.

### Example Question #3 : How To Find The Perimeter Of A Square

What is the perimeter of a square with an area of ?

**Possible Answers:**

**Correct answer:**

1. Find the side lengths:

2. Use the side lengths to find the perimeter:

### Example Question #4 : How To Find The Perimeter Of A Square

Find the perimeter of a square whose area is .

**Possible Answers:**

**Correct answer:**

To solve, you must first find the side length.

Then, you must multiply the side length by 4 since there are 4 sides. Thus,

In this case, volume and perimeter were the same numerical value, but this won't always be the case.

### Example Question #3 : How To Find The Perimeter Of A Square

Find the perimeter of a square with side length .

**Possible Answers:**

**Correct answer:**

To find perimeter, simply multiply side length by . Thus,

### Example Question #5 : How To Find The Perimeter Of A Square

The area of a square is , what is the perimeter of the square?

**Possible Answers:**

**Correct answer:**

Since the sides of a square are all the same, the area of a square can be found by Therefore, the side of the square must be The perimeter of a square can be found by adding up all of the four sides: