{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"9818f672-940e-5973-940f-a76d3f9175c6","task_key":"prealgebra--test--9818f672-940e-5973-940f-a76d3f9175c6","task_revision_id":"1","upstream_id":"","short_description":"$P$ is the midpoint of $\\overline{BD}$. $AP = BP = 4$, $\\overline{AP} \\perp…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"$P$ is the midpoint of $\\\\overline{BD}$. $AP = BP = 4$, $\\\\overline{AP} \\\\perp \\\\overline{BD}$, $\\\\overline{BD} \\\\perp \\\\overline{DC}$, $\\\\overline{AB} \\\\perp \\\\overline{BC}$. In simple radical form, what is the perimeter of pentagon $ABCDP$? [asy]\\nsize(150); defaultpen(linewidth(0.8)); import geometry;\\npair A = origin, B = (4,4), C = (12,-4), D = (4,-4), P = (4,0);\\ndraw(A--P--B--cycle);\\ndraw(B--D--C--cycle);\\ndraw(rightanglemark(A,B,C,15));\\ndraw(rightanglemark(A,P,B,15));\\ndraw(rightanglemark(B,D,C,15));\\nlabel(\\\"$A$\\\",A,SW); label(\\\"$B$\\\",B,N); label(\\\"$C$\\\",C,SE); label(\\\"$D$\\\",D,SW); label(\\\"$P$\\\",P,E); label(\\\"$4$\\\",A--P,S); label(\\\"$4$\\\",B--P,E);\\n\\n[/asy]\",\"type\":\"Prealgebra\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}