Rectangle A B C D has A B=4 and B C=3. Segment E F is constructed through B so that \overline{E F} \perp \overline{D B}, and A and C lie on \overline{D E} and \overline{D F}, respectively. What is E F ?
Answer Choices
A. 9
B. 10
C. \dfrac{125}{12}
D. \dfrac{103}{9}
E. 12