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Elementary Geometry

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by Aman verma » Fri May 21, 2010 8:53 am
Q: A triangle is formed by joining three points P , Q , R on sides AB , BC , CA respectively of Triangle ABC . Then what is the area of Triangle ABC ?

I. The area of Triangle PQR is 6 cm^2

II. P, Q, R are the mid points of the sides AB , BC , CA respectively.
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Source: — Data Sufficiency |
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by liferocks » Fri May 21, 2010 8:58 am
From 1
we know the area of PRQ but no info about the relation between triangle ABC and PQR...not sufficient

From 2
Since P, Q, R are the mid points of the sides AB , BC , CA respectively ,area of triangle pqr=1/4th of area of ABC
but no info on area of PRQ...not sufficient

combining area of ABC=4*area of PQR=24..sufficient

Ans option C
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by gmatmachoman » Fri May 21, 2010 9:48 am
liferocks wrote:From 1
we know the area of PRQ but no info about the relation between triangle ABC and PQR...not sufficient

From 2
Since P, Q, R are the mid points of the sides AB , BC , CA respectively ,area of triangle pqr=1/4th of area of ABC
but no info on area of PRQ...not sufficient

combining area of ABC=4*area of PQR=24..sufficient

Ans option C
Agreed that C is the best option... Now that can u plz tell me how u arrived that PQR is similar to ABC...Just got rusty with basics of similarity!!

I am aware that ration of areas of similar triangles is square of the ratio of the proportional sides..

But plz do let me how PQR & ABC became similar...( I am know its is similar...but forgot the path)
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by liferocks » Fri May 21, 2010 6:32 pm
attached the explanation... sorry for the horrible handwriting and image...but I am really lazy to draw online .And for proving pqr similar to ABC..try using the parallel lines.

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by gmatmachoman » Fri May 21, 2010 9:04 pm
@LR "sis" (hahahhaa...Remember that???) Congrats for scoring half a ton Thanks....

Yeah thx for the explanation.!
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by liferocks » Sat May 22, 2010 4:04 am
gmatmachoman wrote:@LR "sis" (hahahhaa...Remember that???) Congrats for scoring half a ton Thanks....

Yeah thx for the explanation.!
You are welcome govardhan sir!!
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by Aman verma » Sun May 23, 2010 8:28 am
OAC.
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