Question 7
$ABCD$ is a rectangular sheet of paper that has been folded so that corner $B$ is matched with point $B'$ on edge $\overline{AD}.$ The crease is $\overline{EF},$ where $E$ is on $\overline{AB}$ and $F$ is on $\overline{CD}.$ The dimensions $AE = 8,$ $BE = 17,$ and $CF = 3$ are given. The perimeter of rectangle $ABCD$ is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$
