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Geometry

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by Jim@StratusPrep » Tue Aug 19, 2014 4:45 am
Please post the question in forum and not in the doc and I will be happy to answer.
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by GMATGuruNY » Tue Aug 19, 2014 4:56 am
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∆ACD:
Since each side has a length of 3, ∆ACD is equilateral.
Area of an equilateral triangle = (s²/4)√3.
Thus, the area of ∆ACD = (3²/4)√3 = (9/4)√3.

∆ABE:
∆ABE is a 30-60-90 triangle.
In a 30-60-90 triangle, the sides are in the following ratio:
1 - √3 - 2.
Since AB=1, BE=√3, as shown in the figure above.
Thus, the area of ∆ABE = (1/2)bh = (1/2)(AB)(BE) = (1/2)(1)(√3) = (√3)/2.

BCDE:
∆ACD - ∆ABE = (9/4)√3 - (√3)/2 = (9/4)√3 - (2/4)√3 = (7/4)√3.

The correct answer is B.
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by j_shreyans » Tue Aug 19, 2014 6:58 am
Hi ,

Can you pls advise about the ratio.

1 - √3 - 2.

Thanks ,

Shreyans
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by [email protected] » Tue Aug 19, 2014 10:48 am
Hi j_shreyans,

The GMAT tests a variety of concepts regarding right triangles. One of those concepts involves the rules behind a 30/60/90 triangle.

In a 30/60/90, the ratio of the side lengths is 1:√3:2

This means that the side across from the 90 degree angle is 2 times the length of the side across from the 30 degree angle. The side across from the 60 degree angles is √3 times the length of the side across from the 30 degree angle.

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by GMATinsight » Tue Aug 19, 2014 11:11 am
j_shreyans wrote:Hi ,

Can you pls advise about the ratio.

1 - √3 - 2.

Thanks ,

Shreyans
Hi j_Shreyan

Please check the following link to understand more about 30-60-90 Triangle

https://www.regentsprep.org/Regents/math ... Ltri30.htm

Please note that this is a MUST KNOW Concept for GMAT Geometry Questions
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by j_shreyans » Wed Aug 20, 2014 3:09 am
Hello Guys ,

Thanks to all for the help....

Shreyans
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