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We have triangle $\triangle ABC$ where $AB = AC$ and $AD$ is an altitude. Meanwhile, $E$ is a point on $AC$ such that $AB \parallel DE.$ If $BC = 12$ and the area of $\triangle ABC$ is $180,$ what is the area of $ABDE$?

 Jul 15, 2019
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See the following image......

 

Let  A = (6,30)   B = (0, 0)   C = ( 12,0)   D  = (6,0)    and AD  = 30

 

Since ED is parallel to AB.....then ang;e EDC  = angle ABC

And angle ACB  = angle ECD

So triangle ABC will be similar to triangle EDC

And  the base of EDC  = DC is 1/2 of base BC....so

 

The area of triangle EDC  = Area of triangle ABC * (scale factor of EDC to ABC)^2  =

 

!80 * (1/2)^2  =   180 * (1/4)  = 45 units^2

 

So....[ ABDE]  = [ ABC ] - [EDC]  =  180 - 45   = 135 units^2

 

 

cool cool cool

 Jul 15, 2019

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