{"status": "success", "data": {"description_md": "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 $m+n$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Rhombus <span class=\"katex--inline\">PQRS</span> is inscribed in rectangle <span class=\"katex--inline\">ABCD</span> so that vertices <span class=\"katex--inline\">P</span>, <span class=\"katex--inline\">Q</span>, <span class=\"katex--inline\">R</span>, and <span class=\"katex--inline\">S</span> are interior points on sides <span class=\"katex--inline\">\\overline{AB}</span>, <span class=\"katex--inline\">\\overline{BC}</span>, <span class=\"katex--inline\">\\overline{CD}</span>, and <span class=\"katex--inline\">\\overline{DA}</span>, respectively. It is given that <span class=\"katex--inline\">PB=15</span>, <span class=\"katex--inline\">BQ=20</span>, <span class=\"katex--inline\">PR=30</span>, and <span class=\"katex--inline\">QS=40</span>. Let <span class=\"katex--inline\">m/n</span>, in lowest terms, denote the perimeter of <span class=\"katex--inline\">ABCD</span>. Find <span class=\"katex--inline\">m+n</span>.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "1991 AIME Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/91_aime_p13", "prev": "/problem/91_aime_p11"}}