2010 AMC 10A Problem 19

Equiangular hexagon ABCDEF has side lengths AB=CD=EF=1 and BC=DE=FA=r. The area of \triangle ACE is 70\% of the area of the hexagon. What is the sum of all possible values of r?

\textbf{(A)}\ \frac{4\sqrt{3}}{3} \qquad \textbf{(B)} \frac{10}{3} \qquad \textbf{(C)}\ 4 \qquad \textbf{(D)}\ \frac{17}{4} \qquad \textbf{(E)}\ 6

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