{"status": "success", "data": {"description_md": "Let $ABCD$ be a rectangle and let $\\overline{DM}$ be a segment perpendicular to the plane of $ABCD$. Suppose that $\\overline{DM}$ has integer length, and the lengths of $\\overline{MA},\\overline{MC},$ and $\\overline{MB}$ are consecutive odd positive integers (in this order). What is the volume of pyramid $MABCD?$\n\n$\\textbf{(A) }24\\sqrt5 \\qquad \\textbf{(B) }60 \\qquad \\textbf{(C) }28\\sqrt5\\qquad \\textbf{(D) }66 \\qquad \\textbf{(E) }8\\sqrt{70}$\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>Let  <span class=\"katex--inline\">ABCD</span>  be a rectangle and let  <span class=\"katex--inline\">\\overline{DM}</span>  be a segment perpendicular to the plane of  <span class=\"katex--inline\">ABCD</span> . Suppose that  <span class=\"katex--inline\">\\overline{DM}</span>  has integer length, and the lengths of  <span class=\"katex--inline\">\\overline{MA},\\overline{MC},</span>  and  <span class=\"katex--inline\">\\overline{MB}</span>  are consecutive odd positive integers (in this order). What is the volume of pyramid  <span class=\"katex--inline\">MABCD?</span> </p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }24\\sqrt5 \\qquad \\textbf{(B) }60 \\qquad \\textbf{(C) }28\\sqrt5\\qquad \\textbf{(D) }66 \\qquad \\textbf{(E) }8\\sqrt{70}</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": "2021 AMC 12B Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/21_amc12B_p15", "prev": "/problem/21_amc12B_p13"}}