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Equilateral Triangle Question

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Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 00:30
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A
B
C
D
E

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Pls help.
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Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 02:58
mbaMission wrote:
Pls help.


D

The larger area =36square root3
the smaller area=9square root3

So the area of the border=27square root 3
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Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 03:06
How did you get the length of bigger triangle?

sondenso wrote:
mbaMission wrote:
Pls help.


D

The larger area =36square root3
the smaller area=9square root3

So the area of the border=27square root 3

Kudos [?]: 117 [0], given: 11

Manager
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Joined: 01 Aug 2008
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Kudos [?]: 161 [0], given: 2

Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 03:51
sondenso wrote:
mbaMission wrote:
Pls help.


D

The larger area =36square root3
the smaller area=9square root3

So the area of the border=27square root 3



How to calculate the larger area?
_________________

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Do not answer without sharing the reasoning behind ur choice
-----------------------------------------------------------
Working on my weakness : GMAT Verbal
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Ask:
Why, What, How, When, Where, Who
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Kudos [?]: 161 [0], given: 2

2 KUDOS received
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Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 04:10
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Attachment:
solution.jpg
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refer to the attachment.

For smaler triangle, s = 18 / 3 =6
Hieght = √(6^2 + 3^2) = 3√3
Area = 1/2 * 6 * 3√3 = 9√3

For larger traingle, given DQ = √3
Angle QBD = 30 degree (since QB will bisect angle CBA)
Angle QDA = 90 degree, and hence angle DQB = 60

sides of 30-60-90 triangle are always in ratio of 1:√3:2
since DQ = √3
=> DB = √3 * √3 = 3
and QB = 2√3 = AP

Hence, base BC = 6 + 3 + 3 = 12
Height = 3√3 + √3 + 2√3 = 6√3
Area = 1/2 * 12 * 6√3 = 36√3

Diff = 27√3

OA is D.

Please let me know if you need more explanation
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Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 04:39
bigoyal wrote:
Attachment:
solution.jpg


refer to the attachment.

For smaler triangle, s = 18 / 3 =6
Hieght = √(6^2 + 3^2) = 3√3
Area = 1/2 * 6 * 3√3 = 9√3

For larger traingle, given DQ = √3
Angle QBD = 30 degree (since QB will bisect angle CBA)
Angle QDA = 90 degree, and hence angle DQB = 60

sides of 30-60-90 triangle are always in ratio of 1:√3:2
since DQ = √3
=> DB = √3 * √3 = 3
and QB = 2√3 = AP

Hence, base BC = 6 + 3 + 3 = 12
Height = 3√3 + √3 + 2√3 = 6√3
Area = 1/2 * 12 * 6√3 = 36√3

Diff = 27√3

OA is D.

Please let me know if you need more explanation


gr8 job ! thanks mate :wink:
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Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 22:50
I think the height of the smaller traingle should be 5.
By using Pythagoras theorem....

(Height)^2 + (Base)^2 = (Hypot..)^2
h^2 + 3^2 = 6^2
or H=5.
How is it 3sqrt(3) ???????????????

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Re: Equilateral Triangle Question [#permalink]

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New post 07 Jun 2009, 23:36
mdfrahim wrote:
I think the height of the smaller traingle should be 5.
By using Pythagoras theorem....

(Height)^2 + (Base)^2 = (Hypot..)^2
h^2 + 3^2 = 6^2
or H=5.
How is it 3sqrt(3) ???????????????


Altitude of equilateral triangle is (sqr rt 3) / 2 X (length of side)
_________________

==============================================
Do not answer without sharing the reasoning behind ur choice
-----------------------------------------------------------
Working on my weakness : GMAT Verbal
------------------------------------------------------------
Ask:
Why, What, How, When, Where, Who
==============================================

Kudos [?]: 161 [0], given: 2

Director
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Re: Equilateral Triangle Question [#permalink]

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New post 08 Jun 2009, 02:23
mdfrahim wrote:
I think the height of the smaller traingle should be 5.
By using Pythagoras theorem....

(Height)^2 + (Base)^2 = (Hypot..)^2
h^2 + 3^2 = 6^2
or H=5.
How is it 3sqrt(3) ???????????????


You are calculating it incorrectly.
h^2 + 3^2 = 6^2
or, h^2 = 36 - 9 = 27
or, h = √27 = 3√3
_________________

ISB 2011-12 thread | Ask ISB Alumni @ ThinkISB
All information related to Indian candidates and B-schools | Indian B-schools accepting GMAT scores
Self evaluation for Why MBA?

Kudos [?]: 902 [0], given: 56

Re: Equilateral Triangle Question   [#permalink] 08 Jun 2009, 02:23
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