AMC 10 Step by Step
2004 AMC 10BProblem 18P16-20~5 minPrint

In the right triangle ACE\triangle ACE , we have AC=12AC=12 , CE=16CE=16 , and EA=20EA=20 . Points BB , DD , and FF are located on ACAC , CECE , and EAEA , respectively, so that AB=3AB=3 , CD=4CD=4 , and EF=5EF=5 . What is the ratio of the area of DBF\triangle DBF to that of ACE\triangle ACE ?

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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.