Rectangle A B C D has A B=8 and B C=6. Point M is the midpoint of diagonal \overline{A C}, and E is on \overline{A B} with \overline{M E} \perp \overline{A C}. What is the area of \triangle A M E ?

**Answer Choices**

A. \dfrac{65}{8}

B. \dfrac{25}{3}

C. 9

D. \dfrac{75}{8}

E. \dfrac{85}{8}