The thing is to find an expression for this kind of problem you need to use trial and error to find some insight into what that expression could be. For this problem, you would need a quadratic optimizer to find local maximums (for 2 variables e.g. x, y) of the derivatives.

In short, when you do this for similar problems the insight you should observe is that the longer side is x times longer than the shorter side, where x is the additional cost of the shorter side.

In this problem, the shorter sides are 3/2 or 1.5 times more "expensive" than the longer sides.

Therefore the longer side is 270m and the shorter side is 180m. For the total area of 48600m^2.