What is the area of the triangle ABC?

Points M and N are sides' midpoints.
BN ⊥ CM;
BN = 8cm and CM = 12cm

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I know, that the answer is 64 cm^2, but I need a solution step by step.

1 Answer
CW
Oct 31, 2017

area of DeltaABC=64 " cm"^2

Explanation:

Let |ABC| denote area of DeltaABC
As AM:AN=AB:AC, => MN and BC are parallel,
=> DeltaABC and DeltaAMN are similar,
as AM:AB=1:2,
|AMN| : |ABC|=1:2^2=1:4
=> |AMN|:|MNCB|=1:3
given BN is perpendicular to CM,
=> |MNCB|=(BN*CM)/2=(8*12)/2=48
=> |AMN|=(|MNCB|)/3=48/3=16
=> |ABC|=|AMN|+|MNCB|=16+48=64 " cm"^2

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