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

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Manager
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If an equilateral triangle and a square have the same area, [#permalink]

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New post 16 Jun 2006, 15:15
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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)

Please explain your answer.

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.
VP
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New post 16 Jun 2006, 18:22
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
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New post 16 Jun 2006, 19:20
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, 19:20
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If an equilateral triangle and a square have the same area,

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