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# Geometry

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Geometry [#permalink]  04 Oct 2013, 10:14
Hi Everyone,

I need urgent help in solving the question attached to this mail

Thank you.

Best regards,
KitanUrchmann
Attachments

Gmat-2sample questions.docx [26.08 KiB]

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Re: Geometry [#permalink]  04 Oct 2013, 18:39
Expert's post
KitanUrchmann wrote:
Hi Everyone,

I need urgent help in solving the question attached to this mail

Thank you.

Best regards,
KitanUrchmann

AB = Side of larger triangle - Altitude of smaller triangle = 1 - Altitude of smaller triangle

We know the relation between the side and the altitude of an equilateral triangle: Altitude = \frac{\sqrt{3}}{2}*Side
Altitude of larger triangle = \frac{\sqrt{3}}{2}*1 = Side of smaller triangle
Altitude of smaller triangle = \frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{2}*1 = \frac{3}{4}

AB = 1 - 3/4 = 1/4 = 0.25
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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Intern Joined: 15 Jul 2012 Posts: 33 Followers: 0 Kudos [?]: 1 [0], given: 5 Re: Geometry [#permalink] 21 Oct 2013, 04:22 VeritasPrepKarishma wrote: KitanUrchmann wrote: Hi Everyone, I need urgent help in solving the question attached to this mail I anticipate your prompt responses. Thank you. Best regards, KitanUrchmann AB = Side of larger triangle - Altitude of smaller triangle = 1 - Altitude of smaller triangle We know the relation between the side and the altitude of an equilateral triangle: Altitude = \frac{\sqrt{3}}{2}*Side Altitude of larger triangle = \frac{\sqrt{3}}{2}*1 = Side of smaller triangle Altitude of smaller triangle = \frac{\sqrt{3}}{2}*\frac{\sqrt{3}}{2}*1 = \frac{3}{4} AB = 1 - 3/4 = 1/4 = 0.25 See the idea what I got is for 60degree = square root 3 times 30Degree & same way for 90 degree = 2 times 30 degree. i.e. 1:root3:2.... In this case i have understood root3/2 on a larger altitude. Now to find a side opposit to 60degree in smaller altitude, we have been given only 90degree side root3/2.. so how you calculated please tell. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4777 Location: Pune, India Followers: 1116 Kudos [?]: 5062 [0], given: 164 Re: Geometry [#permalink] 22 Oct 2013, 20:52 Expert's post anu1706 wrote: See the idea what I got is for 60degree = square root 3 times 30Degree & same way for 90 degree = 2 times 30 degree. i.e. 1:root3:2.... In this case i have understood root3/2 on a larger altitude. Now to find a side opposit to 60degree in smaller altitude, we have been given only 90degree side root3/2.. so how you calculated please tell. What you wrote is hard to understand. I am assuming you are talking about the small 30-60-90 triangle which includes side AB as the side opposite to the 30 degree angle. You know the hypotenuse is 1/2 (since it is half of side 1 of the equilateral triangle. ) The side opposite 60 degree angle is half of the side is the smaller equilateral triangle. The side of the smaller equilateral triangle is altitude of the larger triangle which is \sqrt{3}/2 * 1. So half of this altitude will be \sqrt{3}/4 AB^2 = (1/2)^2 -(\sqrt{3}/4)^2 = 1/16 So AB = 1/4 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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Intern
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Re: Geometry [#permalink]  22 Oct 2013, 22:31
VeritasPrepKarishma wrote:
anu1706 wrote:

See the idea what I got is for 60degree = square root 3 times 30Degree & same way for 90 degree = 2 times 30 degree. i.e. 1:root3:2....
In this case i have understood root3/2 on a larger altitude. Now to find a side opposit to 60degree in smaller altitude, we have been given only 90degree side root3/2.. so how you calculated please tell.

What you wrote is hard to understand. I am assuming you are talking about the small 30-60-90 triangle which includes side AB as the side opposite to the 30 degree angle.
You know the hypotenuse is 1/2 (since it is half of side 1 of the equilateral triangle. )
The side opposite 60 degree angle is half of the side is the smaller equilateral triangle. The side of the smaller equilateral triangle is altitude of the larger triangle which is \sqrt{3}/2 * 1. So half of this altitude will be \sqrt{3}/4

AB^2 = (1/2)^2 -(\sqrt{3}/4)^2 = 1/16
So AB = 1/4

What I simply wanted to explain is that for 30-60-90 triangle sides are in the ratio of x:rt3x:2x means rt3 is multiplied by x only and not by 2x. Hope i am clear and correct me if i am wrong. So to calculate any side one has to multiply by X only which is side opposite to 30degree.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 4777
Location: Pune, India
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Re: Geometry [#permalink]  22 Oct 2013, 23:26
Expert's post
anu1706 wrote:
VeritasPrepKarishma wrote:
anu1706 wrote:

See the idea what I got is for 60degree = square root 3 times 30Degree & same way for 90 degree = 2 times 30 degree. i.e. 1:root3:2....
In this case i have understood root3/2 on a larger altitude. Now to find a side opposit to 60degree in smaller altitude, we have been given only 90degree side root3/2.. so how you calculated please tell.

What you wrote is hard to understand. I am assuming you are talking about the small 30-60-90 triangle which includes side AB as the side opposite to the 30 degree angle.
You know the hypotenuse is 1/2 (since it is half of side 1 of the equilateral triangle. )
The side opposite 60 degree angle is half of the side is the smaller equilateral triangle. The side of the smaller equilateral triangle is altitude of the larger triangle which is \sqrt{3}/2 * 1. So half of this altitude will be \sqrt{3}/4

AB^2 = (1/2)^2 -(\sqrt{3}/4)^2 = 1/16
So AB = 1/4

What I simply wanted to explain is that for 30-60-90 triangle sides are in the ratio of x:rt3x:2x means rt3 is multiplied by x only and not by 2x. Hope i am clear and correct me if i am wrong. So to calculate any side one has to multiply by X only which is side opposite to 30degree.

Yes the sides of a 30-60-90 are in the ratio 1:\sqrt{3}:2
Since the side opposite 90 is 1/2, the side opposite 30 will be 1/4.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save \$100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

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Re: Geometry   [#permalink] 22 Oct 2013, 23:26
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