{"status": "success", "data": {"description_md": "The angles in a particular triangle are in arithmetic progression, and the side lengths are $4,5,x$. The sum of the possible values of $x$ equals $a+\\sqrt{b}+\\sqrt{c}$ where $a, b$, and $c$ are positive integers. What is $a+b+c$?\n\n$\\textbf{(A)}\\ 36\\qquad\\textbf{(B)}\\ 38\\qquad\\textbf{(C)}\\ 40\\qquad\\textbf{(D)}\\ 42\\qquad\\textbf{(E)}\\ 44$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>The angles in a particular triangle are in arithmetic progression, and the side lengths are  <span class=\"katex--inline\">4,5,x</span> . The sum of the possible values of  <span class=\"katex--inline\">x</span>  equals  <span class=\"katex--inline\">a+\\sqrt{b}+\\sqrt{c}</span>  where  <span class=\"katex--inline\">a, b</span> , and  <span class=\"katex--inline\">c</span>  are positive integers. What is  <span class=\"katex--inline\">a+b+c</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 36\\qquad\\textbf{(B)}\\ 38\\qquad\\textbf{(C)}\\ 40\\qquad\\textbf{(D)}\\ 42\\qquad\\textbf{(E)}\\ 44</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2013 AMC 12A Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12A_p13", "prev": "/problem/13_amc12A_p11"}}