If the north-south sides have length a then the east-west sides have length 360/a.
Cost of the a sides = $60a and the cost of the other sides = $7200/a.
Total cost C=60a+7200/a. Differentiate:
dC/da=60-7200/a2=0 at max or min.
60a2=7200, a2=120m2, a=10.95m (approx).
360/√120=32.86m (approx).
NS sides have a length of 10.95m and EW sides have a length of 32.86m.
Note that this equalises the cost of the NS sides and the EW sides ($657.27).