2010 AMC 12A 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 \qquad \textbf{(B)}\ 33 \qquad \textbf{(C)}\ 35 \qquad \textbf{(D)}\ 36 \qquad \textbf{(E)}\ 37

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