Question

Each side of a square is increased 6 inches. When this happens, the area is multiplied by 9. How many inches in the side of the original square?

Please explain the answer, words confuse me :

Answer 1

Let L represent the side length of the original square.

Note that:

• L² = A
• (L + 6)² = 9A

1. Square root both sides:

• (L + 6)² = 9 x L²
• => √(L + 6)² = √9 x L²

2. Simplify the RHS:

• => L + 6 = 3 x L
• => L + 6 = 3L

3. Subtract L from each side.

• => 6 = 2L

4. Divide 2 both sides.

• => L = 3 inches

Double check:

• Area of square with 3 inches as side length: 3² = 9 in²
• Area of square with 9 inches as side length: 9² = 81 in²

=> 81 ÷ 9 = 9 (True)

This shows that the area of the original square is 9 times smaller than the increased square.

Answer 2

x = 3 inches

Explanation:

Let x = the side of the original square, so the area is x²

After increasing, the side becomes x + 6. so the area becomes (x + 6)²

The area is multiplied by 9 means

(x + 6)² = 9 * x²

Take a square root, get

x + 6 = 3 * x

2x = 6

x = 3 inches