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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 is parallel to  DE.  If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?

 Dec 16, 2020
 #1
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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 is parallel to  DE.  If BC = 15 and the area of triangle ABC is 200, what is the area of ABDE?

 

[ABDE] = 3/4[ABC]  smiley

 Dec 16, 2020
 #2
avatar+117724 
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Area ABC  = (1/2) BC * AD

200  = (1/2) 15 * AD

400  = 15 * AD

400 / 15  = AD

80/3  = AD

 

See the following  image :

 

 

Since  AB is parallel to DE.....triangle  EDC   is  similar to triangle ABC

And  DC  and   BC   are corresponding  sides

Sinc AB = AC....then AD  bisects BC...so

DC =(1/2) BC

So the scale factor  of  EDC to ABC  = 1/2

So the area  of  EDC to ABC =  (scale factor)^2  (area of ABC ) =  (1/4) (200)   = 50 = [EDC ]

 

So   [ ABDE  ]  =  [ ABC ] - [EDC ] =   200  - 50   =   150

 

cool cool cool

 Dec 16, 2020

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