Question 1131139
If longest side of barn is used, 120 feet, and x is the portion along the barn side, then  {{{0<x<120}}}, and area for the corral becomes  {{{x(80-x/2)}}}.  The maximum for this expression can be found:


{{{x(80-x/2)=0}}}

The zeros,  0 and 160.
Exactly in the middle,  {{{x=80}}}


The other dimension:
{{{(160-80)/2}}}

{{{40}}}



Dimensions for maximum area:
80 and 40.


Maximum Corral Area:
3200 ft^2