Question 945343
A square shape will maximize the area of a rectangle.  Cut the fencing into three equal parts.  One more part of equal size will be the barn, not needing the available fence material.



<b>MORE DETAILS</b>


A, for area
w, width
L, length
Assuming 1*L will be against the barn
-
{{{L+2w=650}}}, the amount of fence material to form the rectangular enclosure;
{{{A=wL}}}, basic formula for area;



Use the fencing equation to find a formula for L.
{{{L=650-2w}}}


Substitute for L in the area equation.
{{{highlight(A=w(650-2w))}}}   OR    {{{highlight(A=-2w^2+650w)}}}
-
Area A is a function of w.  This is a parabolic, or quadratic function, and based on the
features of the equation, you know A has a maximum value...
Do the rest.