She only needs 3 sides
take half for the side opposite the river, and divide the remaining part in to two for the other two sides, now we can do the work, but if you have to do more than one of these, a rectangle where one side is free (against a river, a side of a barn, whatever) half is for opposite side, the rest split in two gives other two sides
if we put say y as the side opposite the river, and x as the adjacent sides, then you are told that x+x+y=600 i.e. 2x+y=600
the area is A=xy and you want it to be as large as possible
solve for y and get y=600−2x
then A(x)=x(600−2x)=600x−2x2 and base on that the answer would be 45000
