1958 AHSME Problem 43

\overline{AB} is the hypotenuse of a right triangle ABC. Median \overline{AD} has length 7 and median \overline{BE} has length 4. The length of \overline{AB} is:

\textbf{(A)}\ 10\qquad \textbf{(B)}\ 5\sqrt{3}\qquad \textbf{(C)}\ 5\sqrt{2}\qquad \textbf{(D)}\ 2\sqrt{13}\qquad \textbf{(E)}\ 2\sqrt{15}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.