Question

Stacey 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 the area of the original square. What was the side length of the original square?
A) 1 in.
B) 2 in.
C) 6 in.
D) 12 in.

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
but x cannot be 2 since the side length of the smaller square will be negative.

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

Answer 2

Answer:

6 is the answer

Step-by-step explanation: