Question 258860
{{{A=L*W}}}
For a rectangle, the perimeter is
{{{P=2*(L+W)=500}}}
{{{L+W=250}}}
{{{L=250-W}}}
Substitute this into the area equation,
{{{A=(250-W)W=250W-W^2}}}
To find the maximium area, take the derivative and set it to zero.
{{{dA/dW=250-2W=0}}}
{{{d2A/dw2=-2}}} so you know that the value you get is a maximum (2nd derivative test).
{{{250-2W=0}}}
{{{ 2W=250}}}
{{{W=125}}}
{{{L=250-W=125}}}
The rectangle with the most area is actually a 125' x 125' square.