{"status": "success", "data": {"description_md": "A rectangular box $P$ has distinct edge lengths $a$, $b$, and $c$. The sum of the lengths of\nall $12$ edges of $P$ is $13$, the sum of the areas of all $6$ faces of $P$ is $\\dfrac{11}{2}$, and the volume of $P$ is $\\dfrac{1}{2}$. What is the length of the longest interior diagonal connecting two vertices of $P$?\n\n$\\textbf{(A)}~2\\qquad\\textbf{(B)}~\\frac{3}{8}\\qquad\\textbf{(C)}~\\frac{9}{8}\\qquad\\textbf{(D)}~\\frac{9}{4}\\qquad\\textbf{(E)}~\\frac{3}{2}$", "description_html": "<p>A rectangular box  <span class=\"katex--inline\">P</span>  has distinct edge lengths  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">c</span> . The sum of the lengths of<br/>\nall  <span class=\"katex--inline\">12</span>  edges of  <span class=\"katex--inline\">P</span>  is  <span class=\"katex--inline\">13</span> , the sum of the areas of all  <span class=\"katex--inline\">6</span>  faces of  <span class=\"katex--inline\">P</span>  is  <span class=\"katex--inline\">\\dfrac{11}{2}</span> , and the volume of  <span class=\"katex--inline\">P</span>  is  <span class=\"katex--inline\">\\dfrac{1}{2}</span> . What is the length of the longest interior diagonal connecting two vertices of  <span class=\"katex--inline\">P</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}~2\\qquad\\textbf{(B)}~\\frac{3}{8}\\qquad\\textbf{(C)}~\\frac{9}{8}\\qquad\\textbf{(D)}~\\frac{9}{4}\\qquad\\textbf{(E)}~\\frac{3}{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": "2023 AMC 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10B_p18", "prev": "/problem/23_amc10B_p16"}}