1964 AHSME Problem 38

The sides PQ and PR of \triangle PQR are respectively of lengths 4 inches, and 7 inches. The median PM is 3\frac{1}{2} inches. Then QR, in inches, is:

\textbf{(A) }6\qquad \textbf{(B) }7\qquad \textbf{(C) }8\qquad \textbf{(D) }9\qquad \textbf{(E) }10

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