Question 329416
THe perimeter of a rectangle is,
{{{P=2L+2W=356}}}
{{{L+W=178}}}
The area of a rectangle is,
{{{A=L*W}}}
From the perimeter equation,
{{{L=178-W}}}
Substitute into the area equation,
{{{A=(178-W)W}}}
Now the  area is a function of one variable.
To find the maximum, take the derivative wrt W and set it equal to zero.
{{{A=178W-W^2}}}
{{{dA/dW=178-2W=0}}}
{{{2W=178}}}
{{{W=89}}}
Then from above,
{{{L=178-89=89}}}
The maximum area for a given perimeter is obtained using a square.
{{{Amax=89^2=7921}}}sq.ft.