{"status": "success", "data": {"description_md": "**POTD February 19, 2024**\n\nLet $ABCD$ be a tetrahedron such that edges $AB$, $AC$, and $AD$ are mutually perpendicular. Let the areas of triangles $ABC$, $ACD$, and $ADB$ be denoted $5$, $6$, and $7$, respectively. If the area of triangle $BCD$ can be written as $\\sqrt{a}$ where $a$ is a positive integer, find $a$.", "description_html": "<p><strong>POTD February 19, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">ABCD</span> be a tetrahedron such that edges <span class=\"katex--inline\">AB</span>, <span class=\"katex--inline\">AC</span>, and <span class=\"katex--inline\">AD</span> are mutually perpendicular. Let the areas of triangles <span class=\"katex--inline\">ABC</span>, <span class=\"katex--inline\">ACD</span>, and <span class=\"katex--inline\">ADB</span> be denoted <span class=\"katex--inline\">5</span>, <span class=\"katex--inline\">6</span>, and <span class=\"katex--inline\">7</span>, respectively. If the area of triangle <span class=\"katex--inline\">BCD</span> can be written as <span class=\"katex--inline\">\\sqrt{a}</span> where <span class=\"katex--inline\">a</span> is a positive integer, find <span class=\"katex--inline\">a</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #73", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}