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Is the perimeter of equilateral triangle T equal to the

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Is the perimeter of equilateral triangle T equal to the [#permalink]

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02 Apr 2012, 03:10
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Difficulty:

45% (medium)

Question Stats:

65% (02:09) correct 35% (00:37) wrong based on 17 sessions

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Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

How come the answer is B?
[Reveal] Spoiler: OA

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Re: Is the perimeter of equilateral triangle T equal to the [#permalink]

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02 Apr 2012, 03:50
enigma123 wrote:
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

How come the answer is B?

okay they have approximated then only its possible. It might be mentioned to take pi as 3
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Re: Is the perimeter of equilateral triangle T equal to the [#permalink]

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02 Apr 2012, 20:48
This is a tricky one

Let's say t = a side of the equilateral triangle T
P = perimeter
C = circumference

Statement I

Sum of the lengths of a side of T and the radius of C is 9.
-> t + r = 9 => r = 9 - t
-> perimeter = 3t
-> circumference = 2(pi) (9-t)
-> 3t = 2(pi)(9-t)
-> 3t = 18pi - 2(pi)t
-> 3t + 2(pi)t = 18pi
Without doing the actual calculation, you should be able to infer that they can equal to each other, which means that perimeter and the circumference can equal to each other. Unfortunately this information is rather useless because it doesn't narrow down your answer. This statement essentially says that (could be) P < C or P = C or P > C

Statement II

The length of a side of T is equal to the diameter of C.

This statement sets up a distinct relationship
-> 3t & t*pi
Since pi is greater than 3, the circumference of the circle C cannot equal to perimeter of the triangle T. 3t cannot be greater than t*pi (because t > 0). Therefore Sufficient

Statement 2 on its own conclusively proves that they cannot equal to each other, but statement 1 doesn't. Therefore, the answer has to be (B)

This is how I see it, but I could be wrong. I think it's way more complicated than it needs to be which always makes me nervous about my answer. Let me know if I'm wrong somewhere.
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Re: Is the perimeter of equilateral triangle T equal to the [#permalink]

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03 Apr 2012, 05:33
Expert's post
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9 --> we can split 9, between the lengths of a side and the radius, so that the perimeter to be equal to the circumference as well as not to be equal. Not sufficient.

(2) The length of a side of T is equal to the diameter of C --> we have fixed relationship between the side and the radius, hence we can say whether the perimeter equals to the circumference. Sufficient.

To elaborate more: question asks whether $$3a=2\pi{r}$$, where $$a$$ is the length of a side of triangle T and $$r$$ is the radius of C. Given: $$a=2r$$ --> $$perimeter=3a=6r$$ and $$circumference =2\pi{r}\approx{6.28r}$$, so $$P<C$$.

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Re: Is the perimeter of equilateral triangle T equal to the [#permalink]

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03 Apr 2012, 05:49
enigma123 wrote:
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

How come the answer is B?

i hope to try n explain....plz correct me if i am wrong...

P=3t where t is the side of the triangle

1. t+r = 9
clearly not sufficient

2. t=r
so 3r = 2pir...definately no...Hence B along is sufficient to tell that the perimeter is not equal to Circumference
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Re: Is the perimeter of equilateral triangle T equal to the [#permalink]

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03 Apr 2012, 06:03
Expert's post
harshavmrg wrote:
enigma123 wrote:
Is the perimeter of equilateral triangle T equal to the circumference of circle C ?

(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.

How come the answer is B?

i hope to try n explain....plz correct me if i am wrong...

P=3t where t is the side of the triangle

1. t+r = 9
clearly not sufficient

2. t=r
so 3r = 2pir...definately no...Hence B along is sufficient to tell that the perimeter is not equal to Circumference

(2) The length of a side of T is equal to the diameter of C. So, $$t=2r$$. Else is correct.
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Re: Is the perimeter of equilateral triangle T equal to the   [#permalink] 03 Apr 2012, 06:03
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