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Area of Triangle - Need explanations

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by anirudhbhalotia » Wed Dec 01, 2010 7:24 am
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As per the explanation above, EG = 3squareroot3.

But as per the pythagorean theorem isnt EG = 5, since DE = 6, DG = 3??

And then area of triangle is (5x6)/2 = 15?

Pls explain! Thanks!
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by shovan85 » Wed Dec 01, 2010 8:18 am
anirudhbhalotia wrote:Image



As per the explanation above, EG = 3squareroot3.

But as per the pythagorean theorem isnt EG = 5, since DE = 6, DG = 3??

And then area of triangle is (5x6)/2 = 15?

Pls explain! Thanks!
There is a basic formula for area of an equilateral triangle.

A = [squareroot(3)/4]*(a)^2 where a is the side

Put a = 6 then area = 9squareroot3.

As per Pythagorean theorem also it is correct. EG is not 5 as u have mentioned.

EG = sqrt(DE^2 - DG^2)

= sqrt(36 - 9)

=sqrt 27 = 3 sqrt3

Now Area = 1/2 * 3sqrt3 * 6 (as 1.2 * DF * EG) = 9squareroot3.
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by anirudhbhalotia » Wed Dec 01, 2010 6:55 pm
Oh...stupid of me!

36-9 =27 and not 25 as I was calculating in haste!

Thanks!
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