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

 Aug 21, 2019
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See the following image :

 

 

Since DE is parallel to AB, the triangle DEC is similar to triangle BAC

And BC = 12  and DC  = 6

So the base of triangle DEC  is 1/2 that of triangle BAC

So....the scale factor of triangle DEC to triangle BAC  = 1/2

 

So....the area of triangle DEC  =   (scale factor)^2 * (area of triangle BAC)  =

 

(1/2)^2 * (180)   =   (1/4) (180)   =  45

 

So...the area of ABDE  =   area of triagle BAC - area of triangle DEC  =  180 - 45  =  135 

 

 

cool cool cool

 Aug 21, 2019

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