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 $\displaystyle 900 m^2$. He does this using the least amount of fence possible. What are the dimensions of the field.

$\displaystyle \displaystyle A=xy$

$\displaystyle \displaystyle 900=xy$

$\displaystyle \displaystyle y=\frac{900}{x}$

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 $\displaystyle x$ 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?