{"status": "success", "data": {"description_md": "In the diagram, $\\triangle PQR$ is isosceles with $PQ = PR$ and $\\triangle PRS$ is isosceles with $PS = SR = x$. Also, the perimeter of $\\triangle PQR$ is 22, the perimeter of $\\triangle PRS$ is 22, and the perimeter of $PQRS$ is 24. What is the value of $x$?\n\n<center><img class=\"problem-image\" src=\"/static/cayley/2015/crops/15_cayley_p14_fig.png\" alt=\"figure\" width=\"216\"></center>\n\n$\\text{(A)}\\ 7.5\\qquad\\text{(B)}\\ 6.5\\qquad\\text{(C)}\\ 7\\qquad\\text{(D)}\\ 6\\qquad\\text{(E)}\\ 8$\n\n___\n\n**[Cayley](https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf), by [CEMC](https://cemc.uwaterloo.ca/), is licensed under the [CC BY-NC 3.0 DEED](https://creativecommons.org/licenses/by-nc/3.0/). They are not affiliated with or endorse TopsOJ in any way.**\n", "description_html": "<p>In the diagram, <span class=\"katex--inline\">\\triangle PQR</span> is isosceles with <span class=\"katex--inline\">PQ = PR</span> and <span class=\"katex--inline\">\\triangle PRS</span> is isosceles with <span class=\"katex--inline\">PS = SR = x</span>. Also, the perimeter of <span class=\"katex--inline\">\\triangle PQR</span> is 22, the perimeter of <span class=\"katex--inline\">\\triangle PRS</span> is 22, and the perimeter of <span class=\"katex--inline\">PQRS</span> is 24. What is the value of <span class=\"katex--inline\">x</span>?</p>\n<center><img class=\"problem-image\" src=\"/static/cayley/2015/crops/15_cayley_p14_fig.png\" alt=\"figure\" width=\"216\"></center>\n<p><span class=\"katex--inline\">\\text{(A)}\\ 7.5\\qquad\\text{(B)}\\ 6.5\\qquad\\text{(C)}\\ 7\\qquad\\text{(D)}\\ 6\\qquad\\text{(E)}\\ 8</span></p>\n<hr>\n<p><strong><a href=\"https://www.cemc.uwaterloo.ca/contests/past_contests.html#pcf\">Cayley</a>, by <a href=\"https://cemc.uwaterloo.ca/\">CEMC</a>, is licensed under the <a href=\"https://creativecommons.org/licenses/by-nc/3.0/\">CC BY-NC 3.0 DEED</a>. They are not affiliated with or endorse TopsOJ in any way.</strong></p>\n", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "2015 Cayley Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/15_cayley_p15", "prev": "/problem/15_cayley_p13"}}