Why the Formulas Work · Superchallenge problem

In right triangle $ABC$ with the right angle at $C$, the median from $A$ (to the midpoint of $\overline{BC}$) has length $\sqrt{73}$, and the median from $B$ (to the midpoint of $\overline{AC}$) has length $2\sqrt{13}$. Find the length of the hypotenuse $\overline{AB}$.