{"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":"3f32cf2e-ed2b-56a6-bf53-62d07db1be4c","task_key":"geometry--test--3f32cf2e-ed2b-56a6-bf53-62d07db1be4c","task_revision_id":"1","upstream_id":"","short_description":"Triangle $ABC$ and triangle $DEF$ are congruent, isosceles right triangles. The…","config":"geometry","split":"test","body":"{\"level\":\"Level 4\",\"problem\":\"Triangle $ABC$ and triangle $DEF$ are congruent, isosceles right triangles. The square inscribed in triangle $ABC$ has an area of 15 square centimeters. What is the area of the square inscribed in triangle $DEF$? Express your answer as a common fraction.\\n\\n[asy]\\ndraw((0,0)--(2,0)--(0,2)--(0,0)--cycle,linewidth(2));\\ndraw((0,0)--(1,0)--(1,1)--(0,1)--(0,0)--cycle,linewidth(2));\\ndraw((1/8,0)--(1/8,1/8)--(0,1/8),linewidth(1));\\n\\ndraw((3,0)--(5,0)--(3,2)--(3,0)--cycle,linewidth(2));\\ndraw((3+2/3,0)--(3+4/3,2/3)--(3+2/3,4/3)--(3,2/3)--(3+2/3,0)--cycle,linewidth(2));\\ndraw((3+1/8,0)--(3+1/8,1/8)--(3,1/8),linewidth(1));\\n\\nlabel(\\\"A\\\",(0,2),NW);\\nlabel(\\\"B\\\",(0,0),SW);\\nlabel(\\\"C\\\",(2,0),SE);\\n\\nlabel(\\\"D\\\",(3,2),NW);\\nlabel(\\\"E\\\",(3,0),SW);\\nlabel(\\\"F\\\",(5,0),SE);\\n\\n[/asy]\",\"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":[]}