AMC 8 2014 Problem 14

Rectangle $ABCD$ and right triangle $DCE$ have the same area. They are joined to form a trapezoid, as shown. What is $DE$?

$\textbf{(A) }12 \textbf{(B) }13 \textbf{(C) }14 \textbf{(D) }15 \textbf{(E) }16$