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)