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# imagine a picture of an equilateral triangle with sides T

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Manager
Joined: 05 Dec 2005
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Location: Manhattan Beach, CA
imagine a picture of an equilateral triangle with sides T [#permalink]

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30 Apr 2006, 21:29
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(imagine a picture of an equilateral triangle with sides T and a square with sides S)

If the two regions above have the same area, what is the ratio of T:S?

2:3

16:3

4: sq root 3

2: fourth root 3

4: third root 3

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Manager
Joined: 05 Dec 2005
Posts: 92

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Location: Manhattan Beach, CA

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01 May 2006, 12:34
well, i could have told you that :)

how did you solve it?

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SVP
Joined: 01 May 2006
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01 May 2006, 13:15
(1) S^2 = T/2 x (X)

Where :
> X is the lenght of the projected point of the equalateral trinagle /|\

By Pytagore formula:

T^2 = (T/2)^2 + X^2 So, X = T/2 x root(3)

Replaced in (1), it gives:

S^2 = root(3)/4 x T^2

Thus, T/S = 2:fourth root(3)

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VP
Joined: 29 Apr 2003
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03 May 2006, 04:38

Area of an Equliateral triangle = (s^2)*(sqrt(3)/4!

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Manager
Joined: 27 Mar 2006
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03 May 2006, 06:52
Agree with D

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03 May 2006, 06:52
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# imagine a picture of an equilateral triangle with sides T

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