{"status": "success", "data": {"description_md": "Triangle $ABC$ has side lengths $AB=12$, $BC=25$, and $CA=17$. Rectangle $PQRS$ has vertex $P$ on $\\overline{AB}$, vertex $Q$ on $\\overline{AC}$, and vertices $R$ and $S$ on $\\overline{BC}$. In terms of the side length $PQ=w$, the area of $PQRS$ can be expressed as the quadratic polynomial
\n$$\\text{Area}(PQRS)=\\alpha w-\\beta\\cdot w^2 $$ Then the coefficient $\\beta=\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. 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": "

Triangle ABC has side lengths AB=12, BC=25, and CA=17. Rectangle PQRS has vertex P on \\overline{AB}, vertex Q on \\overline{AC}, and vertices R and S on \\overline{BC}. In terms of the side length PQ=w, the area of PQRS can be expressed as the quadratic polynomial
\\text{Area}(PQRS)=\\alpha w-\\beta\\cdot w^2
Then the coefficient \\beta=\\frac{m}{n}, where m and n are relatively prime positive integers. 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.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2015 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/15_aime_II_p08", "prev": "/problem/15_aime_II_p06"}}