P=2l+2w but one length is not used because of the school
32=l+2w and l=32-2w
this is a parabola that opens downward so there is a maximum at (h,k) where h is the "maximizing point" and k is the maximum area
you would ordinarily have a square that is 8 feet by 8 feet but one section of 8 feet is not used
put this 8 feet with the opposite 8 feet to have a rectangle whose measurements are 8 feet by 16 feet by 8 feet by "the school"
A=128 square feet is the maximum area
if you had a rectangle 17 by 7.5 the area would be 17*7.5=127.5 square feet which is less
if you had a rectangle 15 by 8.5 the area would be 15*8.5=127.5 square feet again