In trapezoid $ABCD$ we have $\overline{AB}\parallel \overline{DC}$, $E$ as the midpoint of $\overline{BC}$, and $F$ as the midpoint of $\overline{DA}$. The area of $ABEF$ is $2.5$ times the area of $FECD$. What is $\frac{AB}{DC}$?