Geometry

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Sun Jun 05, 2011 5:42 am

30:60:90 small triangle

12 root 3 : 12 : 24 root 3

What I get is the side of the big equilateral triangle is 24 root 3 + 12

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Source: Beat The GMAT — Problem Solving | Sun Jun 05, 2011 5:42 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Sun Jun 05, 2011 5:49 am

side of square=12
In the bottom left, a right angled triangle is formed. with base angle 60 degree and another base angle 90 degree
thus tan 60 = 12/base side ->base side = 12/root(3) = 4*root(3)
similarly base side of bottom right = 4*root 3.
Side of triangle = 12+4*root (3)+4*root (3) = 12 + 8*root(3)
perimeter = 3*side = 36 + 24*root(3)
IMO D

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MBA.Aspirant: Master | Next Rank: 500 Posts; Posts: 401; Joined: Tue May 24, 2011 1:14 amFollowed by: 5 members; Thanked: 37 times

by MBA.Aspirant » Sun Jun 05, 2011 5:58 am

I'm gonna rule this test

Thanks

So

it's 30:60:90

12/root3 : 12 : 24/root 3

4 root 3 : 12 : 8 root 3

Side of equi triangle = 4 root 3 + 12 + 4 root 3

= 8 root 3 + 12

* 3

24 root 3 + 36

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sunilramu: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Thu Feb 24, 2011 4:47 am; Thanked: 1 times

by sunilramu » Sun Jun 05, 2011 6:14 am

30:60:90 triangle sides conform to ratio x : x.âˆš3 : 2x
=> x.âˆš3 = 12
=> 2x = 12/âˆš3 . 2 = 8âˆš3

So the length of the side of the triangle = 12 + 8âˆš3
=> perimeter = 3(12+8âˆš3) = 36 + 24âˆš3

Sometimes using a/Sin A = b/Sin B = c/Sin C also helps finding sides from angles if we don't remember the 30:60:90 formula.

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sandeep800: Master | Next Rank: 500 Posts; Posts: 126; Joined: Tue Feb 09, 2010 6:37 pmFollowed by: 4 members

by sandeep800 » Sun Jun 05, 2011 10:32 am

D is correct..

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aftableo2006: Senior | Next Rank: 100 Posts; Posts: 99; Joined: Sat Oct 16, 2010 1:55 pm; Thanked: 1 times

by aftableo2006 » Sun Jun 05, 2011 11:10 pm

36+24root3 is the answer

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ashhchdg: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Sun Aug 14, 2011 4:25 am; Thanked: 1 times

by ashhchdg » Sun Aug 14, 2011 9:06 pm

Hi,
30:60:90 triangle sides are in the ratio, x: xâˆš3:2x

so xâˆš3=12 base of the right triangle ---> base of the equilateral triangle= 2(12/âˆš3)+side of square i.e 12
simplifying we get value as 8âˆš3+12.
perimeter of equilateral triangle=3*(8âˆš3+12)---hence ans D

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