Is the perimeter of equilateral triangle T greater than the perimeter : GMAT Data Sufficiency (DS)
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# Is the perimeter of equilateral triangle T greater than the perimeter

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Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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22 Sep 2010, 08:45
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Is the perimeter of equilateral triangle T greater than the perimeter of square S?

(1) The ratio of the area of T to the area of S is $$\sqrt{3} : 1$$.
(2) The ratio of the length of a side of T to a side of S is 2 : 1.
[Reveal] Spoiler: OA

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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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22 Sep 2010, 09:02
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rxs0005 wrote:
Is the perimeter of the equilateral triangle T greater than the perimeter of the square S

The ratio of the area of T to area of S is root (3) : 1

The ratio of length of a side of T to a side of T is 2 : 1

$$P_{equilateral}=3t$$ and $$P_{square}=4s$$, where $$t$$ and $$s$$ are the sides of triangle and square respectively. Question: is $$P_{equilateral}>P_{square}$$. You can notice that if we knew the ratio of the side $$t$$ to the side $$s$$ then we would be able to answer the question.

(1) The ratio of the area of T to area of S is root (3) : 1 --> both the area of the equilateral triangle ($$area_{equilateral}=t^2\frac{\sqrt{3}}{4}$$) and the area of a square ($$area_{square}=s^2$$) can be expressed with their sides, so we could get the ratio of the sides from the ratio of the areas. Sufficient.

(2) The ratio of length of a side of T to a side of S is 2 : 1 --> directly gives us the ratio of the sides. Sufficient.

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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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06 Oct 2010, 07:13
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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30 Sep 2014, 01:13
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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11 Aug 2016, 09:40
Hello from the GMAT Club BumpBot!

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Re: Is the perimeter of equilateral triangle T greater than the perimeter   [#permalink] 11 Aug 2016, 09:40
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