+0  
 
0
39
1
avatar

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
 #1
avatar+98129 
+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

 

 

cool  cool  cool

 Feb 4, 2019

12 Online Users

avatar
avatar
avatar
avatar