# Problem #2332

 2332 In rectangle $ABCD$, $DC=2CB$ and points $E$ and $F$ lie on $\overline{AB}$ so that $\overline{ED}$ and $\overline{FD}$ trisect $\angle ADC$ as shown. What is the ratio of the area of $\triangle DEF$ to the area of rectangle $ABCD$? $[asy] pair A = (0,1), B = (2,1), C = (2,0), D = (0,0); pair E = intersectionpoint(A--B,D--2*dir(60)), F = intersectionpoint(A--B,D--3*dir(30)); draw(A--D--C--B--cycle); draw(E--D--F); label("A",A,N); label("B",B,N); label("C",C,S); label("D",D,S); label("E",E,N); label("F",F,N); [/asy]$ $\textbf{(A)}\ \ \frac{\sqrt{3}}{6}\qquad\textbf{(B)}\ \frac{\sqrt{6}}{8}\qquad\textbf{(C)}\ \frac{3\sqrt{3}}{16}\qquad\textbf{(D)}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{\sqrt{2}}{4}$ This problem is copyrighted by the American Mathematics Competitions.
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