{"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":"98cead55-2ad9-529c-b9b4-33d7dc37f5b8","task_key":"prealgebra--test--98cead55-2ad9-529c-b9b4-33d7dc37f5b8","task_revision_id":"1","upstream_id":"","short_description":"In any isosceles triangle $ABC$ with $AB=AC$, the altitude $AD$ bisects the base…","config":"prealgebra","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"In any isosceles triangle $ABC$ with $AB=AC$, the altitude $AD$ bisects the base $BC$ so that $BD=DC$.\\n\\nAs shown in $\\\\triangle ABC$, $AB=AC=25$ and $BC=14$.  Determine the length of the altitude $AD$.\\n\\n[asy]\\ndraw((0,0)--(14,0)--(7,24)--cycle,black+linewidth(1));\\ndraw((7,24)--(7,0),black+linewidth(1)+dashed);\\ndraw((7,0)--(7,1)--(6,1)--(6,0)--cycle,black+linewidth(1));\\ndraw((5.5,-4)--(0,-4),black+linewidth(1));\\ndraw((5.5,-4)--(0,-4),EndArrow);\\ndraw((8.5,-4)--(14,-4),black+linewidth(1));\\ndraw((8.5,-4)--(14,-4),EndArrow);\\nlabel(\\\"$A$\\\",(7,24),N);\\nlabel(\\\"$B$\\\",(0,0),SW);\\nlabel(\\\"$C$\\\",(14,0),SE);\\nlabel(\\\"$D$\\\",(7,0),S);\\nlabel(\\\"25\\\",(0,0)--(7,24),NW);\\nlabel(\\\"25\\\",(7,24)--(14,0),NE);\\nlabel(\\\"14\\\",(7,-4));\\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":[]}