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In trapezoid ABCD the lengths of the bases AB and CD are 8 and 17 respectively. The legs of the trapezoid are extended beyond A and B to meet at point E. What is the ratio of the area of triangle EAB to the area of trapezoid ABCD?

 Feb 4, 2019

We wil have a larger triangle CDE    and a smaller triangle BAE


And these triangles  are similar  because AB is parallel to CD


Since AB / CD  = 8 /17


Then   8/17  is the scale factor of triangle BAE  to triangle


Let A be the area of  CDE.....


Then the area of BAE =   (8/17)^2 CDE  =    (64/289)CDE  =  (64/289)A


So....the area of the trapezoid ABCD =   


Area of CDE  - Area BAE  = 


A - (64/289)A  =   (225/289)A


So  the ratio of  triangle EAB to trapezoid ABCD =


(64/289)A / [ (225/289) A ]   =



64 /225



cool  cool  cool

 Feb 4, 2019

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