1965 AHSME Problem 12

A rhombus is inscribed in \triangle ABC in such a way that one of its vertices is A and two of its sides lie along AB and AC. If \overline{AC} = 6 inches, \overline{AB} = 12 inches, and \overline{BC} = 8 inches, the side of the rhombus, in inches, is:

\textbf{(A)}\ 2 \qquad \textbf{(B) }\ 3 \qquad \textbf{(C) }\ 3 \frac {1}{2} \qquad \textbf{(D) }\ 4 \qquad \textbf{(E) }\ 5

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