1962 AHSME Problem 39

Two medians of a triangle with unequal sides are 3 inches and 6 inches. Its area is 3 \sqrt{15} square inches. The length of the third median in inches, is:

\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 3 \sqrt{3} \qquad \textbf{(C)}\ 3 \sqrt{6} \qquad \textbf{(D)}\ 6\sqrt{3}\qquad \textbf{(E)}\ 6\sqrt{6}

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