Question

Each side of a square is increased 3 inches. When this happens, the area is multiplied by 25. How many inches in the side of the original square?

Answer 1

Answer:

s = 0.75 inches

Step-by-step explanation:

Let s = side length of the original square

s + 3 = side length of the new square

Area of a square = s²

A = s²

A = (s+3)²

A = s² + 6s + 9

Area multiplied by 25 = 25 * s²

So,

s² + 6s + 9 = 25s²

25s² - s² - 6s - 9 = 0

24s² - 6s - 9 = 0

8s² - 2s - 3 = 0

a = 8

b = -2

c = -3

s = -b ± √b² - 4ac / 2a

= -(-2) ± √(-2)² - 4(8)(-3) / 2(8)

= 2 ± √4 - (-96) / 16

= 2 ± √100 / 16

= 2 ± 10/16

s = 2 + 10/16 or 2-10/16

= 12/16 or -8/16

= 0.75 or -0.5

side length can not be negative

Therefore, s = 0.75

A = s²

A = (0.75)²

= 0.5625

A = (s+3)²

= (0.75+3)²

= 3.75²

= 13.95