Question 114394
Start with defining a variable to represent the length of a side of the original square, let's call it x.

So the area of the original square would be {{{A[o]=x^2}}}.


The new square is 2 cm shorter on each side, so one of the sides must measure {{{x-2}}}, and the area of the new square must be {{{A[n]=(x-2)^2}}}.


But we know that {{{A[o]=A[n]+36cm^2}}}.  Substituting:  {{{x^2=(x-2)^2+36}}}.


Now, expand the binomial, collect terms, and put the equation in standard form.


{{{x^2=x^2-4x+4+36}}}
{{{x^2-x^2=x^2-x^2-4x+40}}}
{{{-4x+40=0}}}
{{{-4x=-40}}}
{{{x=10}}}


So the original square was 10 cm on a side.


Let's check the answer.


Original area {{{10^2=100}}}
New area {{{8^2=64}}}
{{{100-64=36}}}, Check.