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GMAT Geometry
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Author:  questioner [ Thu Jan 26, 2012 4:58 pm ]
Post subject:  Re: math (test 1, question 1): geometry, triangles

Quote:
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?

Author:  Gennadiy [ Thu Jan 26, 2012 5:08 pm ]
Post subject:  Re: math (test 1, question 1): geometry, triangles

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

Author:  questioner [ Wed Mar 14, 2012 3:10 pm ]
Post subject:  Re: math (test 1, question 1): geometry, triangles

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.

Author:  Gennadiy [ Wed Mar 14, 2012 3:19 pm ]
Post subject:  Re: math (test 1, question 1): geometry, triangles

Quote:
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)?

Author:  questioner [ Fri Aug 17, 2012 4:41 pm ]
Post subject:  Re: GMAT Geometry

Can you please explain me what is the calculation for this result? Thanks

Author:  Gennadiy [ Fri Aug 17, 2012 4:44 pm ]
Post subject:  Re: GMAT Geometry

questioner wrote:
Can you please explain me what is the calculation for this result? Thanks
Please, specify which moment (transition) in the calculations in not clear two you and I'll be able to explain it.

Author:  questioner [ Thu Aug 30, 2012 8:40 am ]
Post subject:  Re: GMAT Geometry

What is the inches? Your answer is the square root.

Author:  Gennadiy [ Thu Aug 30, 2012 8:43 am ]
Post subject:  Re: GMAT Geometry

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.

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