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

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Intern
Joined: 19 Oct 2004
Posts: 17
If two sides of a triangle have lengths 2 and 5, which of [#permalink]

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02 May 2007, 11:46
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15% (low)

Question Stats:

74% (01:18) correct 26% (00:19) wrong based on 237 sessions

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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 09 Jun 2014, 08:38, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
Intern
Joined: 26 Feb 2007
Posts: 3

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02 May 2007, 14:47
None b/c the 1 side of a triangle cant be more than the sum of the two other sides. Otherwise it wouldnt be a triangle.

1 side<2 other sides
VP
Joined: 08 Jun 2005
Posts: 1145

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02 May 2007, 15:07
1
KUDOS
you have to know the rule:

"one property that all triangles share is that the sum of the lengths of any two sides is greater then the length of the third side"

x+y>z
z+x>y
y+z>x

x=2
y=5
z=?

2+5>z
z+2>5
5+z>2

from this we know that z has to be - 3>z>7

perimeter = x+y+z

case 1 - z=2
case 2 - z=8
case 3 - z=12

hence the answer is (A) - none
Manager
Joined: 02 May 2007
Posts: 152
Re: GMAT PREP - PS [#permalink]

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02 May 2007, 21:52
lavanya_25 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

Help with this one .

Thanks
Lavanya

(B) it is

The question is "which of the following could be the perimeter of the triangle?"
Senior Manager
Joined: 19 Feb 2007
Posts: 325
Re: GMAT PREP - PS [#permalink]

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03 May 2007, 01:45
kirakira wrote:
lavanya_25 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

Help with this one .

Thanks
Lavanya

(B) it is

The question is "which of the following could be the perimeter of the triangle?"

The ans should be A

Since the third side should be less than the sum of other 2 sides and greater than their difference.

so 3 < Third side <7

so 10 < Perimeter < 14
Manager
Joined: 04 Oct 2006
Posts: 76

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04 May 2007, 05:44
1
This post was
BOOKMARKED
----------------
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
----------------

max of the third side is 2+5 = 7 then the perimeter max is less than 14
min of the third side is 5-2 = 3 then the perimeter min is more than 10

Senior Manager
Joined: 03 May 2007
Posts: 270

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04 May 2007, 08:13
the rule is simple: sum of the lengths of any two sides of triangle have to be greater than the length of the third one.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15948
Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink]

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09 Jun 2014, 08:18
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 39659
Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink]

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09 Jun 2014, 08:38
Expert's post
3
This post was
BOOKMARKED
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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-two-sides-of-a-triangle-have-lengths-2-and-5-which-of-th-163409.html
_________________
Re: If two sides of a triangle have lengths 2 and 5, which of   [#permalink] 09 Jun 2014, 08:38
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