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In triangle △ABC, BE and CF are medians. BE=9, CF=12. If BE is perpendicular to CF, find the area of the triangle △ABC in cm2.

 

 Dec 25, 2020
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Call the intersections of the  medians, D.....this is the centroid

And  BD  =(2/3) BE = (2/3)(9)  = 6

And CF  =  (2/3)CF = (2/3) (12)  = 8

So....triangle DBC is a 6-8-10 right triangle  and its area =  (1/2) (6)(8)  =24

 

If we drew another median from A to BC....it would  divide this triangle into 2 triangles with equal areas.....so   the area of one of these  triangles  =12

 

And this triangle   = 1/6  area of ABC

 

So  [ ABC]  =  6 * 12    = 72

 

 

cool cool cool

 Dec 25, 2020

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