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If two sides of a triangle have lengths 2 and 5, which of

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If two sides of a triangle have lengths 2 and 5, which of [#permalink] New post 19 Nov 2006, 04:54
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If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-two-sides-of-a-triangle-have-lengths-2-and-5-which-of-th-163409.html
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2014, 01:24, edited 1 time in total.
Added the OA.
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Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink] New post 19 Nov 2006, 06:15
Sum of any 2sides should be greater than 3rd side.

Should be A
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Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink] New post 19 Nov 2006, 07:22
A

1) 3rd side would be 2 and 2 + 2 not greater than 5
2) 3rd side is 8 and 2+5 not greater than 8
3) 3rd side is 12 and 2+5 not greater than 12
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Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink] New post 29 Jun 2014, 19:38
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Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink] New post 30 Jun 2014, 01:25
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lfox2 wrote:
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?

I. 9
II. 15
III. 19

(A) None
(B) I only
(C) II only
(D) II and III only
(E) I, II, and III



The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

Therefore:
(5-2) < {third side} < (5+2).

3 < {third side} < 7.

Perimeter = {third side} + 2 + 5 = {third side} + 7.

10 < {perimeter} < 14.

Answer: A.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-two-sides-of-a-triangle-have-lengths-2-and-5-which-of-th-163409.html
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Re: If two sides of a triangle have lengths 2 and 5, which of   [#permalink] 30 Jun 2014, 01:25
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