AMC 12 2010a Problem 14

Nondegenerate $\triangle ABC$ has integer side lengths, $\overline{BD}$ is an angle bisector, $AD = 3$, and $DC=8$. What is the smallest possible value of the perimeter?

\textbf{(A)}\ 30 \textbf{(B)}\ 33 \textbf{(C)}\ 35 \textbf{(D)}\ 36 \textbf{(E)}\ 37