Question 983972
For a rectangle, {{{perimeter=2(length+width)}}} ,
and for a square both measurements are the same {{{side}}} .
So, in this case, for the original rectangle
{{{2(length+width)=32cm}}} <---> {{{length+width=16cm}}} .
If {{{length}}} decreases by {{{1cm}}} , and
if {{{width}}} increases by {{{3cm}}} , we get
{{{length-1cm=side}}} of a square, and
{{{width+3cm=side}}} of the same square.
That means that for the rectangle
{{{length-1cm=width+3cm}}} <---> {{{length=width+4cm}}} .
From {{{system(length+width=16cm,length=width+4cm)}}} , we get
{{{(width+4cm)+width=16cm}}} <---> {{{2(width)+4cm=16cm}}} <---> {{{2(width)=16cm-4cm}}} <---> {{{2(width)=12cm}}} <---> {{{width=12cm/2}}} <---> {{{width=6cm}}} .
I could now find the {{{length}}} for the rectangle, but I don't need that.
I know that if {{{width=6cm}}} for the rectangle, then for the square, 
{{{side=6cm+3cm}}} ---> {{{side=9cm}}} ,
and that makes the area of the square
{{{(9cm)(9cm)=81}}}{{{cm^2}}}.
The area of the square is {{{highlight(81)}}} square centimeters.