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 mc020-1.jpg the area of the original square. What was the side length of the original square?

A = s2
1 in.
2 in.
6 in.
12 in.

Answer 1

Let the original side be s. After cutting 3 in. off the length and 3 in. off the width the new side is s − 3. If the smaller square’s area is 1/4 of the original, then
(s − 3)^2 = (1/4)s^2.
Taking square roots (positive sides): s − 3 = (1/2)s → (1/2)s = 3 → s = 6.
So the original side length was 6 inches.