1991 AIME Problem 12

Rhombus PQRS^{}_{} is inscribed in rectangle ABCD^{}_{} so that vertices P^{}_{}, Q^{}_{}, R^{}_{}, and S^{}_{} are interior points on sides \overline{AB}, \overline{BC}, \overline{CD}, and \overline{DA}, respectively. It is given that PB^{}_{}=15, BQ^{}_{}=20, PR^{}_{}=30, and QS^{}_{}=40. Let m/n^{}_{}, in lowest terms, denote the perimeter of ABCD^{}_{}. Find m+n^{}_{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.