{"status": "success", "data": {"description_md": "A wire is cut into two pieces, one of length $a$ and the other of length $b$. The piece of length $a$ is bent to form an equilateral triangle, and the piece of length $b$ is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is $\\frac{a}{b}$?\n\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{6}}{2}\\qquad\\textbf{(C)}\\ \\sqrt{3} \\qquad\\textbf{(D)}\\ 2\\qquad\\textbf{(E)}\\ \\frac{3\\sqrt{2}}{2}$", "description_html": "<p>A wire is cut into two pieces, one of length  <span class=\"katex--inline\">a</span>  and the other of length  <span class=\"katex--inline\">b</span> . The piece of length  <span class=\"katex--inline\">a</span>  is bent to form an equilateral triangle, and the piece of length  <span class=\"katex--inline\">b</span>  is bent to form a regular hexagon. The triangle and the hexagon have equal area. What is  <span class=\"katex--inline\">\\frac{a}{b}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ \\frac{\\sqrt{6}}{2}\\qquad\\textbf{(C)}\\ \\sqrt{3} \\qquad\\textbf{(D)}\\ 2\\qquad\\textbf{(E)}\\ \\frac{3\\sqrt{2}}{2}</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 10B Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10B_p16", "prev": "/problem/13_amc10B_p14"}}