2001 AMC 10 Problem 24

In trapezoid ABCD, \overline{AB} and \overline{CD} are perpendicular to \overline{AD}, with AB+CD=BC, AB<CD, and AD=7. What is AB\cdot CD?

\textbf{(A)}\ 12 \qquad \textbf{(B)}\ 12.25 \qquad \textbf{(C)}\ 12.5 \qquad \textbf{(D)}\ 12.75 \qquad \textbf{(E)}\ 13

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