Each side of a square is increased 3 inches. When this happens, the area is multiplied by 4. How many inches in the side of the original square?

Answer 1

Sylvia, let x be the side of the original square and y be the area. We start with two equations based on what we are given:

x² = y

(x+3)² = 4y

Now we substitute x² in for y in the second equation and get into standard quadratic form:

(x+3)² = 4x²

(x+3)(x+3) = 4x²

x² + 6x + 9 = 4x²

3x² - 6x - 9 = 0

We factor and solve the quadratic:

(3x + 3)(x - 3) = 0

x= -1,3

Since we can't have a negative length, only one answer makes sense

x = 3 in

Hope this helps!

Answer 2

(x + 3)² = 4x²

x² + 6x + 9 = 4x²

0 = 3x² - 6x - 9

0 = x² - 2x - 3

0 = (x + 1)(x - 3)