{"status": "success", "data": {"description_md": "The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths $2\\sqrt3$, $5$, and $\\sqrt{37}$, as shown, is $\\tfrac{m\\sqrt{p}}{n}$, where $m$, $n$, and $p$ are positive integers, $m$ and $n$ are relatively prime, and $p$ is not divisible by the square of any prime. Find $m+n+p$.
$\\includegraphics[width=119, height=84, totalheight=84]{https://latex.artofproblemsolving.com/2/0/4/2040951aabf67ea7477c8aa658e56ccda3a56492.png}$\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": "

The area of the smallest equilateral triangle with one vertex on each of the sides of the right triangle with side lengths 2\\sqrt3, 5, and \\sqrt{37}, as shown, is \\tfrac{m\\sqrt{p}}{n}, where m, n, and p are positive integers, m and n are relatively prime, and p is not divisible by the square of any prime. Find m+n+p.

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": 6, "problem_name": "2017 AIME I Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/17_aime_I_p14"}}