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