Question 1085081
The area of the square is,
{{{A[s]=s^2}}}
For the rectangle,
{{{W=s-96}}}
{{{L=256+2s}}}
{{{A=L*W}}}
{{{s^2=(s-96)(2s+256)}}}
{{{s^2=2s^2+64s-24576}}}
{{{s^2+64s-24576=0}}}
Complete the square,
{{{s^2+64s+1024-24576=1024}}}
{{{(s+32)^2=24576+1024}}}
{{{(s+32)^2=25600}}}
{{{s+32=0 +- 160}}}
Lengths are never negative.
{{{s=128}}}{{{cm}}}
So then the dimensions of the rectangle are,
{{{W=128-96}}}
{{{W=32}}}{{{cm}}}
and
{{{L=256+2(128)}}}
{{{L=512}}}{{{cm}}}