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# Here's another one: If two sides of a triangle have

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Senior Manager
Joined: 27 Aug 2005
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Here's another one: If two sides of a triangle have [#permalink]

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06 Sep 2005, 20:26
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Here's another one:

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

(1) None
(2) I only
(3) II only
(4) II and III only
(5) I, II and III

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Manager
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06 Sep 2005, 20:56
The third side of the triangle can not be equal or large them the sum of the others sides.

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Senior Manager
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06 Sep 2005, 21:02
It's asking for the perimeter, not the length of the third side.

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Senior Manager
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06 Sep 2005, 21:55
The sum of any two sides of a triangle must be GREATER than the third side.

So, the third side of the triangle must be less than 7 and the perimeter must be less than 14. So number two is the answer....I think

Please correct me if I'm wrong because sometimes I feel like I'm not doing these right.

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Intern
Joined: 04 Sep 2005
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07 Sep 2005, 03:28
2 + 5 = 7
5 - 2 = 3
3 < side < 7
10 < perimeter < 14

(1) none

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Senior Manager
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07 Sep 2005, 07:59
Duh. Thanks.

I'm telling you, my error logs are just embarrassing when I look at them the next day sometimes... I'm terrified of missing such obvious questions on the real test.

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VP
Joined: 13 Jun 2004
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Location: London, UK
Schools: Tuck'08

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07 Sep 2005, 08:57
exactly the same way as Kog

we know that tthe last side has to be > 3 but < 7
so the perimeter has to be :
5+2+3 < P < 5+2+7
10 < P < 14

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Senior Manager
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07 Sep 2005, 11:31
Yup, wasn't doing it right. Thanks for the help guys

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Senior Manager
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15 Jul 2007, 06:58
Can anyone explain why perimeter can not be 9?
Then we could have sides: 2-2-5
It would have been equilateral triangle....
Why not?

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Senior Manager
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15 Jul 2007, 07:09
Caas wrote:
Can anyone explain why perimeter can not be 9?
Then we could have sides: 2-2-5
It would have been equilateral triangle....
Why not?

It is not possible to construct a 2-2-5 triangle. The sum of any two sides must be greater than the third side for any triangle. Here 2+2 < 5. Hence, it is not possible.

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15 Jul 2007, 07:09
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