AHSME 1975 Problem 20

In the adjoining figure triangle $ABC$ is such that $AB = 4$ and $AC = 8$. IF $M$ is the midpoint of $BC$ and $AM = 3$, what is the length of $BC$?

$\textbf{(A)}\ 2\sqrt{26} \textbf{(B)}\ 2\sqrt{31} \textbf{(C)}\ 9 \textbf{(D)}\ 4 + 2\sqrt{13}\\ \textbf{(E)}\ \text{not enough information given to solve the problem}$