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 \(m+n^{}_{}\).

(第九届AIME1991 第12题)