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