{"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":"5b465e46-fa0a-529a-ba16-0dd44c0fec8d","task_key":"prealgebra--test--5b465e46-fa0a-529a-ba16-0dd44c0fec8d","task_revision_id":"1","upstream_id":"","short_description":"In the diagram, $AB,$ $BC,$ $CD,$ $DE,$ $EF,$ $FG,$ $GH,$ and $HK$ all have…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"In the diagram, $AB,$ $BC,$ $CD,$ $DE,$ $EF,$ $FG,$ $GH,$ and $HK$ all have length $4,$ and all angles are right angles, with the exception of the angles at $D$ and $F.$\\n\\n[asy]\\ndraw((0,0)--(0,4)--(4,4)--(4,8)--(6.8284,5.1716)--(9.6569,8)--(9.6569,4)--(13.6569,4)--(13.6569,0)--cycle,black+linewidth(1));\\ndraw((0,0)--(0.5,0)--(0.5,0.5)--(0,0.5)--cycle,black+linewidth(1));\\ndraw((0,4)--(0.5,4)--(0.5,3.5)--(0,3.5)--cycle,black+linewidth(1));\\ndraw((4,4)--(4,4.5)--(3.5,4.5)--(3.5,4)--cycle,black+linewidth(1));\\ndraw((6.8284,5.1716)--(7.0784,5.4216)--(6.8284,5.6716)--(6.5784,5.4216)--cycle,black+linewidth(1));\\ndraw((9.6569,4)--(10.1569,4)--(10.1569,4.5)--(9.6569,4.5)--cycle,black+linewidth(1));\\ndraw((13.6569,4)--(13.1569,4)--(13.1569,3.5)--(13.6569,3.5)--cycle,black+linewidth(1));\\ndraw((13.6569,0)--(13.1569,0)--(13.1569,0.5)--(13.6569,0.5)--cycle,black+linewidth(1));\\nlabel(\\\"$A$\\\",(0,0),W);\\nlabel(\\\"$B$\\\",(0,4),NW);\\nlabel(\\\"$C$\\\",(4,4),S);\\nlabel(\\\"$D$\\\",(4,8),N);\\nlabel(\\\"$E$\\\",(6.8284,5.1716),S);\\nlabel(\\\"$F$\\\",(9.6569,8),N);\\nlabel(\\\"$G$\\\",(9.6569,4),S);\\nlabel(\\\"$H$\\\",(13.6569,4),NE);\\nlabel(\\\"$K$\\\",(13.6569,0),E);\\n[/asy]\\n\\nDetermine the length of $DF.$\\n\\n[asy]\\ndraw((0,0)--(2.8284,-2.8284)--(5.6568,0),black+linewidth(1));\\ndraw((0,0)--(5.6568,0),black+linewidth(1)+dashed);\\ndraw((2.8284,-2.8284)--(3.0784,-2.5784)--(2.8284,-2.3284)--(2.5784,-2.5784)--cycle,black+linewidth(1));\\nlabel(\\\"$D$\\\",(0,0),N);\\nlabel(\\\"$E$\\\",(2.8284,-2.8284),S);\\nlabel(\\\"$F$\\\",(5.6568,0),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":[]}