Question 183805
Your start is correct, you need to do the second part of the problem.
The area of two rectangles is equal
Rectangle 2
L is increased by 8
{{{L=W+4+8}}}
Width is decreased by 4
{{{W=W-4}}}
{{{A=(w-4)(w+12)}}}
Using FOIL method
{{{W^2+12W-4W-48=A}}}
{{{W^2+8W-48=A}}}
Since the Area didn't change from the first Rectangle
{{{W^2+8W-48=W^2+4W}}}
Move all variables to one side and constants to the other
{{{W^2+8W-w^2-4W=48}}}
{{{4W=48}}}
{{{w=12}}}
Since L=W+4
{{{L=12+4=16}}}

Check your answer
{{{(16)(12)=192}}}
{{{(16+8)(12-4)=(24)(8)=192
The solution works