Question 960228
Let the regions dimensions be L and W.
The area of the region is,
{{{L*W=15000}}}
and the amount of fencing used is,
{{{W+L+W=400}}}
{{{2W+L=400}}}
{{{L=400-2W}}}
Substituting,
{{{(400-2W)W=15000}}}
{{{-2W^2+400W=15000}}}
{{{W^2-200W+7500=0}}}
{{{(W-50)(W-150)=0}}}
Two solutions:
{{{W-50=0}}}
{{{W=50}}}
Then,
{{{L=400-2(50)}}}
{{{L=400-100}}}
{{{L=300}}}
50Wx300L
and
{{{W-150=0}}}
{{{W=150}}}
Then,
{{{L=400-2(150)}}}
{{{L=400-300}}}
{{{L=100}}}
150Wx100L