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triangle question

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by Night reader » Mon Dec 20, 2010 2:35 am
In triangle ABC, MN is parallel with BC and AM/AB = 2/3. What is the ratio between the area of triangle AMN and the area of triangle ABC?

A. 2/3
B. 2/9
C. 4/5
D. 4/9
E. 5/9
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by Rahul@gurome » Mon Dec 20, 2010 2:53 am
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Refer to the figure above,
Area of ABC = (1/2)*BC*AE
Area of AMN = (1/2)*MN*AD

As, AM/AB = 2/3 and MN parallel to BC,
  • 1. MN/BC = 2/3
    2. AD/AE = 2/3
Required ratio = (MN*AD)/(BC*AE) = (MN/BC)*(AD/AE) = (2/3)*(2/3) = 4/9

The correct answer is D.
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by minar » Mon Dec 20, 2010 7:45 am
Rahul@gurome,
Your replies are always easy to understand. Thanks for that... :)
I have a quick question on the PS.

What about if I consider ABC and AMN both to be equilateral triangle?
If I do so, I get the same answer (D).
Is my approach wrong?
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by Rahul@gurome » Mon Dec 20, 2010 7:59 am
minar wrote:Rahul@gurome,
Your replies are always easy to understand. Thanks for that... :)
I'm glad to know that. :)
minar wrote:What about if I consider ABC and AMN both to be equilateral triangle?
If I do so, I get the same answer (D).
Is my approach wrong?
For this particular problem the logic is fine and it'll not cause any problem. But always try not to choose any special case. That can mislead you.
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