Question 1028745
So it's a 3 sided rectangle that he needs to build using 500m of fencing.
The area is,
{{{A=L*W}}}
The perimeter of fencing used is,
{{{P=500}}}
{{{2L+W=500}}}
So you can then make area a function of one variable,
{{{W=500-2L}}}
Substituting,
{{{A=L(500-2L)}}}
{{{A=-2L^2+500L}}}
To find the maximum, convert to vertex form:
{{{A=-2(L^2-250L)}}}
{{{A=-2(L^2-250L+125^2)+2(125)^2}}}
{{{A=-2(L-125)^2+31250}}}
So the maximum area of {{{31250}}}{{{m^2}}} occurs when {{{L=125}}}{{{m}}}
Then,
{{{W=500-2(125)}}}
{{{W=500-250}}}
{{{W=250}}}{{{m}}}