Question 1077442
x, distance from highway to side opposite of the highway
y, distance of the side parallel to but opposite of the highway


Fence length to use, {{{2x+y=400}}}


Area to hold, {{{xy}}}


Area, {{{A(x)=x(400-2x)}}}
Parabola shape and equation {{{A(x)=x(400-2x)}}}, with vertex as the maximum point.


{{{x(400-2x)=0}}} gives the roots
{{{x(200-x)=0}}}
{{{system(Roots,x=0,and,x=200)}}}


Maximum A will be at x=100, exactly in the middle of the roots.


{{{2x+y=400}}}
{{{y=400-2x}}}
{{{y=400-2*100}}}
{{{y=400-200}}}
{{{y=200}}}



Dimensions for maximum area:
100 and 200
-
Two sides 100 and one side 200.