Question

Janet has a square piece of cloth. She cuts 3 inches off of the length of the square and 3 inches off of the width. The area of the smaller square is 1/4 of the area of the original square. What was the side length of the original square?

Answer 1

Let the side length of the original square be x, then

1/4 x^2 = (x - 3)^2

x^2 = 4(x^2 - 6x + 9) = 4x^2 - 24x + 36

3x^2 - 24x + 36 = 0

3(x^2 - 8x + 12) = 0

x^2 - 8x + 12 = 0

x^2 - 2x - 6x + 12 = 0

x(x - 2) - 6(x - 2) = 0

(x - 6)(x - 2) = 0

x - 6 = 0 or x - 2 = 0

x = 6 or x = 2

therefore, the side length of the original square is 6 inches.

Hope this helps!