{"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":"43c4a3e6-7aa3-52f0-9cc3-2246ddf49b5d","task_key":"geometry--test--43c4a3e6-7aa3-52f0-9cc3-2246ddf49b5d","task_revision_id":"1","upstream_id":"","short_description":"Two right triangles share a side as follows: [asy]","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Two right triangles share a side as follows: [asy]\\npair pA, pB, pC, pD, pE;\\npA = (0, 0);\\npB = pA + 4 * dir(0);\\npC = pA + 5 * dir(90);\\npD = pB + 4 * dir(90);\\npE = (4 * pA + 5 * pD) / 9;\\ndraw(pA--pB--pC--pA);\\ndraw(pA--pB--pD--pA);\\nlabel(\\\"$A$\\\", pA, SW);\\nlabel(\\\"$B$\\\", pB, SE);\\nlabel(\\\"$C$\\\", pC, NW);\\nlabel(\\\"$D$\\\", pD, NE);\\nlabel(\\\"$E$\\\", pE, 2 * N);\\nlabel(\\\"$4$\\\", pA--pB, S);\\nlabel(\\\"$5$\\\", pA--pC, W);\\nlabel(\\\"$4$\\\", pB--pD, E);\\ndraw(rightanglemark(pB,pA,pC,8));\\ndraw(rightanglemark(pD,pB,pA,8));\\n[/asy] What is the area of $\\\\triangle ABE$?\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}