2004 AIME II Problem 7

A B C D is a rectangular sheet of paper that has been folded so that corner B is matched with point B^{\prime} on edge \overline{A D}. The crease is \overline{E F}, where E is on \overline{A B} and F is on \overline{C D}. The dimensions A E=8, B E=17, and C F=3 are given. The perimeter of rectangle A B C D is m / n, where m and n are relatively prime positive integers. Find m+n.