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

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Intern
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If two sides of a triangle have lengths 2 and 5, which of [#permalink]

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02 May 2007, 10:46
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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, 07:38, edited 2 times in total.
Renamed the topic, edited the question and added the OA.
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02 May 2007, 13:47
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
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02 May 2007, 14:07
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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
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Re: GMAT PREP - PS [#permalink]

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02 May 2007, 20:52
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?"
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Re: GMAT PREP - PS [#permalink]

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03 May 2007, 00:45
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
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04 May 2007, 04:44
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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
----------------

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

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04 May 2007, 07:13
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.
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Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink]

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09 Jun 2014, 07:18
Hello from the GMAT Club BumpBot!

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Re: If two sides of a triangle have lengths 2 and 5, which of [#permalink]

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09 Jun 2014, 07:38
Expert's post
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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

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
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Re: If two sides of a triangle have lengths 2 and 5, which of   [#permalink] 09 Jun 2014, 07:38
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