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

(第二十二届AIME2 2004 第7题)