Question 114255
Let x = the original length of each side of the square.
The original area is then:
{{{A = x^2}}}
Decreasing the sides by 2 cm. (x-2) results in the area being decreased by 36 sq. cm. (A - 36), so you can write:
{{{(x-2)^2 = (A-36)}}} for the new area. Substitute {{{A = x^2}}} and solve for x.
{{{(x-2)^2 = x^2-36}}} Simplify.
{{{x^2-4x+4 = x^2-36}}} Subtract {{{x^2}}} from both sides.
{{{-4x+4 = -36}}} Subtract 4 from both sides.
{{{-4x = -40}}} Divide both sides by -4.
{{{x = 10}}}cm.