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# If a triangle with equil sides, "T", and a square

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Intern
Joined: 23 May 2008
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If a triangle with equil sides, "T", and a square [#permalink]

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05 Dec 2008, 20:23
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If a triangle with equil sides, "T", and a square with sides "S" have the same area, what is the ratio T:S? (GMAT practice test)

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Manager
Joined: 27 May 2008
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05 Dec 2008, 21:13
area of eqil. Triangle = V3/4 T^2 = area of square S^2

So T/S = Sqrt(4/(sqrt(3)))

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Intern
Joined: 05 Dec 2008
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06 Dec 2008, 10:42
Perhaps I'll offer a slightly longer answer to fill in some missing parts:

If S is one side of a square, then the area of the square is S^2
If T is one side of an equilateral triangle, then the area of the triangle is T^2(sqrt3)/4 (you must memorize this formula!)

Since the area of the two shapes are equal, we can say that T^2(sqrt3)/4 = S^2

Our goal is to find the ratio of T:S (aka T/S)

We take our equation T^2(sqrt3)/4 = S^2 and divide both sides by S^2, and divde both sides by (sqrt3)/4 to get:
T^2/S^2 = 4/sqrt3
We're almost there. Now find the square root of both sides to get:

T/S = sqrt[4/sqrt3]
This can be simplified to be 2/sqrt[sqrt3] or to be 2 : sqrt[sqrt3]

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Intern
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08 Dec 2008, 11:59

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Re: Ratio's   [#permalink] 08 Dec 2008, 11:59
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