Convex quadrilateral A B C D has A B=9 and C D=12. Diagonals \overline{A C} and \overline{B D} intersect at E, A C=14, and \triangle A E D and \triangle B E C have equal areas. What is A E ?
Answer Choices
A. \dfrac{9}{2}
B. \dfrac{50}{11}
C. \dfrac{21}{4}
D. \dfrac{17}{3}
E. 6