Suppose we have a rectangle with a side of length L and another side of length (L-x). The area of the rectangle is
[tex]A=L(x-L)=Lx-L^2[/tex]
We impose the condition of maximum
[tex]dA/dL =0[/tex]
Thus [tex]x-2L=0[/tex]
[tex]x=2L[/tex]
Hence the maximum area is when we have a square
[tex]A =L(2L-L) =L^2[/tex]
With a perimeter [tex]P=4L[/tex] we obtain [tex]L=P/4 =260/4=65 feet[/tex]
which gives A =L^2=65*65 =6225 ft^2
