Question 1103039
For a rectangle,
{{{A=L*W}}}
In this case,
{{{W+L+W=2400}}}
{{{2W+L=2400}}}
{{{L=2400-2W}}}
Substituting into the area equation,
{{{A=(2400-2W)W}}}
{{{A=-2W^2+2400W}}}
Get the area into vertex form by completing the square to find the max area.
{{{A=-2(W^2-1200W+600^2)+2(600)^2}}}
{{{A=-2(W-600)^2+2(360000)}}}
{{{A=-2(W-600)^2+720000}}}
So the max area occurs when {{{W=600}}}{{{ft}}} and is equal to {{{720000}}}{{{ft^2}}}
So then from above,
{{{A=L*W}}}
{{{L=720000/600}}}
Solve for L.