{"status": "success", "data": {"description_md": "**POTD May 15, 2024**\n\nLet $ABC$ be a triangle with $AB = 13, BC = 14,$ and $CA = 15.$ Let $l$ be a line passing through two sides of triangle $ABC.$ Line $l$ cuts triangle $ABC$ into two figures, a triangle and a quadrilateral, that have equal perimeter. Given that the maximum possible area of the triangle can be written as $\\frac{m}{n}$ for positive integers $m$ and $n$, find the value of $m+n$.", "description_html": "<p><strong>POTD May 15, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">ABC</span> be a triangle with <span class=\"katex--inline\">AB = 13, BC = 14,</span> and <span class=\"katex--inline\">CA = 15.</span> Let <span class=\"katex--inline\">l</span> be a line passing through two sides of triangle <span class=\"katex--inline\">ABC.</span> Line <span class=\"katex--inline\">l</span> cuts triangle <span class=\"katex--inline\">ABC</span> into two figures, a triangle and a quadrilateral, that have equal perimeter. Given that the maximum possible area of the triangle can be written as <span class=\"katex--inline\">\\frac{m}{n}</span> for positive integers <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span>, find the value of <span class=\"katex--inline\">m+n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #157", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}