{"status": "success", "data": {"description_md": "What is the perimeter of the boundary of the region consisting of all points which can be expressed as $(2u-3w, v+4w)$ with $0\\le u\\le1$, $0\\le v\\le1,$ and $0\\le w\\le1$?\n\n$\\textbf{(A) } 10\\sqrt{3} \\qquad \\textbf{(B) } 13 \\qquad \\textbf{(C) } 12 \\qquad \\textbf{(D) } 18 \\qquad \\textbf{(E) } 16$", "description_html": "<p>What is the perimeter of the boundary of the region consisting of all points which can be expressed as  <span class=\"katex--inline\">(2u-3w, v+4w)</span>  with  <span class=\"katex--inline\">0\\le u\\le1</span> ,  <span class=\"katex--inline\">0\\le v\\le1,</span>  and  <span class=\"katex--inline\">0\\le w\\le1</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 10\\sqrt{3} \\qquad \\textbf{(B) } 13 \\qquad \\textbf{(C) } 12 \\qquad \\textbf{(D) } 18 \\qquad \\textbf{(E) } 16</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": 4, "problem_name": "2023 AMC 10B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10B_p25", "prev": "/problem/23_amc10B_p23"}}