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2004 AMC 10AProblem 20P16-20~6 minPrint
Triangles: Area & PythagoreanSimilar & Congruent TrianglesApply an identity: SFFT, sum of squares, difference of cubes, VietaExploit symmetry to reduce work or pair up objects

Points EE and FF are located on square ABCDABCD so that △BEF\triangle BEF is equilateral. What is the ratio of the area of △DEF\triangle DEF to that of △ABE\triangle ABE ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.