What is the area of the triangle ABC?

Question

What is the area of the triangle ABC?

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

I know, that the answer is $64 c m^{2}$ $64 cm^2$ , but I need a solution step by step.

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Answer 1 · 2017-10-31T02:30:51

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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What is the area of the triangle ABC?

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

I know, that the answer is $64 c m^{2}$ $64 cm^2$ , but I need a solution step by step.

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

What is the area of the triangle ABC?

Points MMM and NNN are sides' midpoints. BNBNBN ⊥ CMCMCM; BN = 8BN=8BN = 8cm and CM = 12CM=12CM = 12cm I know, that the answer is 64 cm^264cm264 cm^2, but I need a solution step by step.

1 Answer

Explanation:

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Impact of this question

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

I know, that the answer is $64 c m^{2}$ $64 cm^2$ , but I need a solution step by step.