### All PSAT Math Resources

## Example Questions

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

The area of square R is 12 times the area of square T. If the area of square R is 48, what is the length of one side of square T?

**Possible Answers:**

4

1

16

2

**Correct answer:**

2

We start by dividing the area of square R (48) by 12, to come up with the area of square T, 4. Then take the square root of the area to get the length of one side, giving us 2.

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

When the side of a certain square is increased by 2 inches, the area of the resulting square is 64 sq. inches greater than the original square. What is the length of the side of the original square, in inches?

**Possible Answers:**

18

15

14

17

16

**Correct answer:**

15

Let x represent the length of the original square in inches. Thus the area of the original square is x^{2}. Two inches are added to x, which is represented by x+2. The area of the resulting square is (x+2)^{2}. We are given that the new square is 64 sq. inches greater than the original. Therefore we can write the algebraic expression:

x^{2} + 64 = (x+2)^{2}

FOIL the right side of the equation.

x^{2} + 64 = x^{2} + 4x + 4

Subtract x^{2 }from both sides and then continue with the alegbra.

64 = 4x + 4

64 = 4(x + 1)

16 = x + 1

15 = x

Therefore, the length of the original square is 15 inches.

If you plug in the answer choices, you would need to add 2 inches to the value of the answer choice and then take the difference of two squares. The choice with 15 would be correct because 17^{2} -15^{2} = 64.

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

If the area of a square is 25 inches squared, what is the perimeter?

**Possible Answers:**

25

15

20

10

Not enough information

**Correct answer:**

20

The area of a square is equal to length times width or length squared (since length and width are equal on a square). Therefore, the length of one side is or The perimeter of a square is the sum of the length of all 4 sides or

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