We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
79
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+101871 
+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

5 Online Users