Domain for this optimization problem

A farmer puts fencing around a rectangular field. He then uses more fencing to subdivide the field into three smaller "pens," such that each of the three pens are . He does this using the least amount of fence possible. What are the dimensions of the field.

To find the domain, I would have thought that you needed to set each variable to be greater than or equal to zero, doing that would mean that can be any number greater than zero. Is that the correct domain?

Edit: And in the context of this problem, that would mean the only values I would test are where the slope equals zero to find the maximum/minimums?