Problem Solving

First, I'll preface the presentation of this problem by saying that I *did* search for this problem, and I *did* find the problem (or something very similar, at least), but I did *not* understand the solution as it was presented. So, before everyone gets bent out of shape, please understand that I am re-introducing this problem to get a new perspective, and maybe some better understanding of the solution. If you don't feel like responding, that's fine, but scolding isn't necessary either.

I encountered the following problem on a CAT through the Manhattan GMAT site.

Which of the following is a possible length for side AB of triangle ABC if AC = 6 and BC = 9?

I. 3
II. 9*sqrt(3)
III. 13.5

Choices:
A) I only
B) II only
C) III only
D) II and III
E) I, II and III

I should also add that, in the earlier presentation of this problem, choice II was simply '9', rather than '9*sqrt(3)'. I understand how this might have occurred because, when I copied the problem from the screen within the CAT, the radical sign did not copy over. The previous individual might not have noticed this, or they simply mis-typed it.

Ans: C

The explanation provided in that Manhattan GMAT CAT was confusing to me, because it would preclude the existence of a "famous" right triangle...