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The centroid of triangle ABC is G.  Given AD = 15 and BE = \(25\), find the area of triangle ABC.

 

 Apr 27, 2022
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By a property of the  medians

 

EG = 25 (1/3)  =  25 /  3

AG =  15 (2/3)  = 10

 

Since triangle AGE is right...its area =   (1/2)product of legs EG and AG   =  (1/2)(25/3)(10) = 250 / 6

 

And by another median property, this area  = 1/6 the area of ABC

 

So

 

[ ABC ]  =  6 (250  /  6)  =   250 units ^2

 

 

cool cool cool

 Apr 27, 2022

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