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# Is the perimeter of the equilateral triangle T greater than

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Is the perimeter of the equilateral triangle T greater than [#permalink]  22 Sep 2010, 08:45
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Difficulty:

25% (medium)

Question Stats:

78% (02:02) correct 22% (01:09) wrong based on 64 sessions
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
[Reveal] Spoiler: OA

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Re: Geometry DS [#permalink]  22 Sep 2010, 09:02
Expert's post
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: Geometry DS [#permalink]  06 Oct 2010, 07:13
D it is
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Perimeter of triangle [#permalink]  13 May 2012, 04:24
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.

Any idea how the answer is D guys?
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Kudos [?]: 24469 [0], given: 2680

Re: Perimeter of triangle [#permalink]  13 May 2012, 04:28
Expert's post
enigma123 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.

Any idea how the answer is D guys?

Merging similar topics.
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Re: Perimeter of triangle   [#permalink] 13 May 2012, 04:28
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