Question 249008
Let the length of the side of the original square be x.
The area of the original square  is:
{{{A = x^2}}}
The area of the new rectangle is:
{{{A = (x+6)*(x-4)}}}
{{{A = x^2+2x-24}}} But this is equal to the area of the original square, so...
{{{x^2 = x^2+2x-24}}} Subtract {{{x^2}}} from both sides.
{{{0 = 2x-24}}} Add 24 to both sides.
{{{2x = 24}}} Divide both sides by 2.
{{{x = 12}}}
The dimensions of the square are: 12 X 12