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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?

Guest Feb 4, 2019

#1**+1 **

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

CPhill Feb 4, 2019