AMC 12 2009b Problem 13

Triangle $ABC$ has $AB = 13$ and $AC = 15$, and the altitude to $\overline{BC}$ has length $12$. What is the sum of the two possible values of $BC$?

\textbf{(A)}\ 15 \textbf{(B)}\ 16 \textbf{(C)}\ 17 \textbf{(D)}\ 18 \textbf{(E)}\ 19