{"status": "success", "data": {"description_md": "Let $ABCD$ be a rectangle with $AB = 30$ and $BC = 28$. Point $P$ and $Q$ lie on $\\overline{BC}$ and $\\overline{CD}$ respectively so that all sides of $\\triangle{ABP}, \\triangle{PCQ},$ and $\\triangle{QDA}$ have integer lengths. What is the perimeter of $\\triangle{APQ}$?\n\n$\\textbf{(A) } 84 \\qquad \\textbf{(B) } 86 \\qquad \\textbf{(C) } 88 \\qquad \\textbf{(D) } 90 \\qquad \\textbf{(E) } 92$", "description_html": "<p>Let  <span class=\"katex--inline\">ABCD</span>  be a rectangle with  <span class=\"katex--inline\">AB = 30</span>  and  <span class=\"katex--inline\">BC = 28</span> . Point  <span class=\"katex--inline\">P</span>  and  <span class=\"katex--inline\">Q</span>  lie on  <span class=\"katex--inline\">\\overline{BC}</span>  and  <span class=\"katex--inline\">\\overline{CD}</span>  respectively so that all sides of  <span class=\"katex--inline\">\\triangle{ABP}, \\triangle{PCQ},</span>  and  <span class=\"katex--inline\">\\triangle{QDA}</span>  have integer lengths. What is the perimeter of  <span class=\"katex--inline\">\\triangle{APQ}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 84 \\qquad \\textbf{(B) } 86 \\qquad \\textbf{(C) } 88 \\qquad \\textbf{(D) } 90 \\qquad \\textbf{(E) } 92</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 10A Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc10A_p18", "prev": "/problem/23_amc10A_p16"}}