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# If an equilateral triangle and a square have the same area,

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Manager
Joined: 17 Dec 2005
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If an equilateral triangle and a square have the same area, [#permalink]  16 Jun 2006, 14:15
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If an equilateral triangle and a square have the same area, what is ratio of one side of the equilateral triangle and one side of the square?

a) 2:3

b) 16:3

c) 4 : sqrt(3)

d) 2 : 3^(1/4)

e) 4 : 3^(1/4)

Additionally, how anyone else notice how much geometry the GMATPrep has? The OG11 and the supplement materials don't touch on geometry all that much. On my practice test, I hit like 5 geometry problems within the first 15. Anyone have any ideas on how to quickly improve on geometry?

Thanks.
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VP
Joined: 02 Jun 2006
Posts: 1267
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[#permalink]  16 Jun 2006, 17:22
d) 2 : 3^(1/4)

Triangle side =t Square side = s

For triangle altitude = tx sqrt(3)/2

Ratio required = t/s

Given Ar. Square = Ar. of triangle

s^2 = 1/2x t x t x sqrt(3)/2
s^2 = t^2 x sqrt(3) /4

or (t^2)/(s^2) = 4/sqrt(3)

i.e t/s = sqrt(4/sqrt(3))
i.e. t/s = 2/3^(1/4)

t:s = 2: 3^(1/4)
CEO
Joined: 20 Nov 2005
Posts: 2913
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 18

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[#permalink]  16 Jun 2006, 18:20
D

Area of triangle = (x^2) * SQRT(3)/4
Area of square = y^2

(x^2) * SQRT(3)/4 = y^2
i.e x^2/y^2 = 4/SQRT(3)
x/y = 2/3^(1/4)
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

[#permalink] 16 Jun 2006, 18:20
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# If an equilateral triangle and a square have the same area,

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