Answer: D

Small Hint:

Let the legs opposite $A$ and $B$ have squared lengths $u$ and $v$

Big Hint:

Use the two median formulas together with the Pythagorean relation for the hypotenuse

Solution:

Let $a=BC,$ $b=CA,$ and $c=AB.$ Since the right angle is at $C,$ $c^2=a^2+b^2.$ The median formulas give $$\begin{aligned} 4(7^2) &=a^2+4b^2,\\ 4(4^2) &=4a^2+b^2. \end{aligned}$$ Solving yields $a^2=4$ and $b^2=48.$ Therefore $$\begin{aligned} AB=c &=\sqrt{a^2+b^2}\\ &=\sqrt{52}=2\sqrt{13}. \end{aligned}$$

Thus, the correct answer is D.