{"status": "success", "data": {"description_md": "Two sides of a triangle have lengths $10$ and $15$.  The length of the altitude to the third side is the average of the lengths of the altitudes to the two given sides.  How long is the third side?\n\n$\\textbf{(A)}\\ 6 \\qquad\\textbf{(B)}\\ 8 \\qquad\\textbf{(C)}\\ 9 \\qquad\\textbf{(D)}\\ 12 \\qquad\\textbf{(E)}\\ 18$", "description_html": "<p>Two sides of a triangle have lengths  <span class=\"katex--inline\">10</span>  and  <span class=\"katex--inline\">15</span> .  The length of the altitude to the third side is the average of the lengths of the altitudes to the two given sides.  How long is the third side?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 6 \\qquad\\textbf{(B)}\\ 8 \\qquad\\textbf{(C)}\\ 9 \\qquad\\textbf{(D)}\\ 12 \\qquad\\textbf{(E)}\\ 18</span> </p>\n<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 10A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10A_p16", "prev": "/problem/13_amc10A_p14"}}