A Square was altered so that one side is increased by 9 inches in the other side is decreased by 2 inches. The area of the resulting rectangle is 60 in.² what was the area of the original Square?

Let s represent the length of any one side of the original square. The longer side of the resulting rectangle is s + 9 and the shorter side s - 2.

The area of this rectangle is (s+9) (s-2) = 60 in^2.

This is a quadratic equation and can be solved using various methods. Let's rewrite this equation in standard form: s^2 + 7s - 18 = 60, or:

s^2 + 7s - 78 = 0. This factors as follows: (s+13) (s-6) = 0, so that s = - 13 and s = 6. Discard s = - 13, since the side length cannot be negative. Then s = 6, and the area of the original square was 36 in^2.