Question

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?

Answer 1

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.