Question 975411
rectangle has l and w
l*w is a maximum
l*(24-l) is maximum
24l -l^2 is maximum when?
-l^2+24l=y

x=-b/2a = -24/-2=12

The rectangle with maximum area is a square with length and width 12.  The area is 144 sq ft.

{{{graph(300,200,-15,15,-15,200,-x^2+24x)}}}