Problem
2014 AMC 10B Problem 15
In rectangle ABCD, DC=2 \cdot CB 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]](/static/aops/7f364224de78eb6e54231a4b75dfe360d6af253f.png)
\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}
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