Question 252964
If the length of one side is X, the other side is 36 - X, so that 2X + (72 -2x) = 72.
The Area is X(36 -X)= 36X + X^2
For that to be greatest requires dy/dx to be 0
ie 36 - 2X = 0
x = 18
The largest area is for a square pool 18 yards on each side.