
Min area using calculus
So the problem is this.
It is required to enclose a rectangular field with a fence and then divide it into two lots by a fence parallel to one of the sides. If the area is given, what is the ratio of the two sides so that the total amount of fence is at a min?

Call the length of the side the last fence is parallel to "x" and the length of the other side "y". What is the area in terms of x and y? You have 3 fences of length x and two of length y. What is the total length of the fences.