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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, 09:45
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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, 10:02
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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, 08:13
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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30 Sep 2014, 02:13
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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11 Aug 2016, 10:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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14 Mar 2017, 17:15
Can someone give another example of the first statement? I am still unclear about it.
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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14 Mar 2017, 17:20
Bunuel wrote:
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.

What I'm unclear about is the formula t squared=root 3 divided by four. Does that formula give the ratio of the sides? Like if the sides of an equilateral were 2 : 2 : 2 then would 2^2 times root divided by four equal the ratio of the side of a square- does that mean the side of a square is 2 root 3 then? Two squared= 4 times root 3 divided by four then cancels out to root 3 then multiply 2 by root 3 and that's the length of the side of the square?
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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14 Mar 2017, 21:35
Nunuboy1994 wrote:
Bunuel wrote:
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.

What I'm unclear about is the formula t squared=root 3 divided by four. Does that formula give the ratio of the sides? Like if the sides of an equilateral were 2 : 2 : 2 then would 2^2 times root divided by four equal the ratio of the side of a square- does that mean the side of a square is 2 root 3 then? Two squared= 4 times root 3 divided by four then cancels out to root 3 then multiply 2 by root 3 and that's the length of the side of the square?

First of all please use math formulas (check here: https://gmatclub.com/forum/rules-for-po ... l#p1096628).

Next, $$t^2*\frac{\sqrt{3}}{4}$$ is a formula for an area of an equilateral triangle with the length of a side equal to t.
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Re: Is the perimeter of equilateral triangle T greater than the perimeter [#permalink]

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14 Mar 2017, 21:47
We can find the sides of triangle and square using a and b separately. Hence it is D.

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

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15 Mar 2017, 01:53
rxs0005 wrote:
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.

Let the side for the triangle be t and square be s

St 1:\sqrt{3}/4 *t^2/s^2 = \sqrt{3}

or t/s = 2
or t = 2s

therefroe the perimeter for the triangle = 3t = 6s
area of suare = 4s
hence 6s>4s

St 2: t/s = 2 or t = 2s
therefroe the perimeter for the triangle = 3t = 6s
area of suare = 4s
hence 6s>4s

Option D
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Re: Is the perimeter of equilateral triangle T greater than the perimeter   [#permalink] 15 Mar 2017, 01:53
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