Question 77286
Let the side of the origimal square be of length x.
The original area is then {{{x^2}}} After decreasing the original side length by 2 (x-2), the new area is decreased by 36 sq.cm.({{{x^2-36}}}).
So, you can write:
{{{(x-2)^2 = x^2-36}}} Simplify and solve for x.
{{{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}}}
The length of the side of the original square is 10 cm.

Check:
Original area is 10X10 = 100 sq.cm.
The new area is (10-2)X(10-2) = 8X8 = 64 sq.cm
The difference: 100-64 = 36 sq.cm.