1991 AIME Problem 12

Rhombus P Q R S is inscribed in rectangle A B C D so that vertices P, Q, R, and S are interior points on sides \overline{A B}, \overline{B C}, \overline{C D}, and \overline{D A}, respectively. It is given that PB=15, BQ=20, PR=30, and Q S=40. Let \frac{m}{n}, in lowest terms, denote the perimeter of A B C D. Find m+n.