{"status": "success", "data": {"description_md": "*This is a user suggested problem. The TopsOJ staff thanks and gives full credit to [ Maximilian113](https://www.topsoj.com/users/Maximilian113/profile) for their contribution.*\n\n****\nLet $ABC$ be a triangle with perimeter $15$, and suppose that $\\displaystyle 16[ABC]^2 = (AB+BC+CA) \\cdot AB \\cdot BC \\cdot CA.$ If $[ABC]$ is of the form $\\frac{m\\sqrt{p}}{n},$ where $m$ and $n$ are relatively prime, positive integers, and $p$ is not divisible by the square of a prime, find $m+n+p.$", "description_html": "

This is a user suggested problem. The TopsOJ staff thanks and gives full credit to Maximilian113 for their contribution.

Let ABC be a triangle with perimeter 15, and suppose that \\displaystyle 16[ABC]^2 = (AB+BC+CA) \\cdot AB \\cdot BC \\cdot CA. If [ABC] is of the form \\frac{m\\sqrt{p}}{n}, where m and n are relatively prime, positive integers, and p is not divisible by the square of a prime, find m+n+p.

", "hints_md": "Try Heron's.", "hints_html": "

Try Heron’s.

", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "M1: A Triangle Problem", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}