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 Post subject: Re: GMAT Geometry
PostPosted: Fri Apr 05, 2013 12:35 am 
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5) The lengths of the sides of a 30-60-90 triangle are always in the ratio of 1 : √3 : 2.
If we divide the height of the triangle by √3, we will have the length of the short side. Multiplying the value of the short side by 2 will give us the length of the hypotenuse:
Hypotenuse = (12 / √3) × 2= 24/√3 = (24√3)/3= 8√3.
This makes no sense to me. Why is it divided by the square root of 3?


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 Post subject: Re: GMAT Geometry
PostPosted: Fri Apr 05, 2013 12:36 am 
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questioner wrote:
This makes no sense to me. Why is it divided by the square root of 3?
Take a look at the shaded triangle:
Image
It's bottom left angle is 60⁰ as an angle of the equilateral triangle.
It's bottom right angle is 90⁰ (as complimentary to the angle of the square).
Therefore it is a 90⁰-60⁰-30⁰ triangle. There is the following property of such triangles: the sides are in 2:√3:1 ratio. We know that the side of the square, which is also the leg of this right triangle, equals 12. So
hypotenuse : 12 = 2 : √3.
hypotenuse = (2/√3) × 12
hypotenuse = 24/√3
hypotenuse = (24 × √3)/(√3 × √3)
hypotenuse = 24√3/3
hypotenuse = 8√3


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 Post subject: Re: GMAT Geometry
PostPosted: Fri Apr 05, 2013 12:39 am 
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I solved for the perimeter of the smaller equilateral triangle, which is 36. I believe it would help candidates if there was some indication as to which equilateral triangle for which the question is asking - or just don't provide 36 as a possible answer. Thank you.


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 Post subject: Re: GMAT Geometry
PostPosted: Fri Apr 05, 2013 12:40 am 
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if there was some indication as to which equilateral triangle for which the question is asking
The question statement deals with only one equilateral triangle in it – the one that surrounds the square. So the question statement asks about that specific triangle:
Quote:
... what is the perimeter of the equilateral triangle (in inches)?


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 Post subject: Re: GMAT Geometry
PostPosted: Fri Apr 05, 2013 12:43 am 
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What is the inches? Your answer is the square root.


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 Post subject: Re: GMAT Geometry
PostPosted: Fri Apr 05, 2013 12:46 am 
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questioner wrote:
What is the inches? Your answer is the square root.
Inch is a unit of length. All answer choices are given in inches as it is implied at the end of the question statement. (24√3 + 36) is the numerical value.

The perimeter of the triangle equals (24√3 + 36) inches.


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