Question 249084
{{{W = 2L - 5}}}
{{{A = L * W = 88}}}
.
Substitute
{{{A = L * (2L-5)}}} 
{{{88 = 2L^2 - 5L}}}
.
Subtract 88 from both sides
{{{0 = 2L^2 -5L -88}}}
so
{{{2L^2 -5L - 88 = 0}}}
.
Can you factor this?  Yes.
.
{{{(2L +11)(L - 8) = 0}}}
.
So our candidate solutions are L = -5.5 and L = 8.
.
A negative number for the side of the rectangle is nonsense.  So our answer is L = 8.
.
Recall
{{{W = 2L - 5}}}
so
{{{W = 2*8 - 5 = 16 - 5 = 11}}}
.
With L = 8 and W = 11, the area = 88.
So we're done.