# If the measure of one side of a square is increased by 2 centimeters and the measure of the adjacent side is decreased by 2 centimeters, the area of the resulting rectangle is 32 square centimeters. How do you find the measure of one side of the square?

Oct 27, 2016

Let the initial side length of the square be $x$. Then the new lengths are $x + 2$ and $x - 2$.

$\left(x + 2\right) \left(x - 2\right) = 32$

${x}^{2} + 2 x - 2 x - 4 = 32$

${x}^{2} - 4 = 32$

${x}^{2} = 36$

$x = 6$

Hence, the side of the square measured $6$ centimetres.

Hopefully this helps!