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# Triangle ABC has sides 15, 17, and X. If X is an integer,

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SVP
Joined: 03 Feb 2003
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Triangle ABC has sides 15, 17, and X. If X is an integer, [#permalink]

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05 Jul 2004, 00:42
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Triangle ABC has sides 15, 17, and X. If X is an integer, then what are the greatest and the smallest possible X?

Kudos [?]: 308 [0], given: 0

Manager
Joined: 02 Jun 2004
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Location: Kiev, Ukraine

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05 Jul 2004, 00:51
stolyar wrote:
Triangle ABC has sides 15, 17, and X. If X is an integer, then what are the greatest and the smallest possible X?

From triangle inequalities, we get 17 - 15 < x < 15 + 17, => 3 and 31, respectively, are minimum and maximum possible values of X.
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Director
Joined: 05 Jul 2004
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05 Jul 2004, 00:51
We can use Triangle enequalities:
Sum of two sides will always be greater that the third side.
Using that, we get
15 + 17 > x --> x < 32
15 + x > 17 --> x > 2
17 + x > 15 --> x > -2

We have to consider those points which satisfy all 3 inequalities
so, we get 2 < x < 32

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SVP
Joined: 03 Feb 2003
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05 Jul 2004, 01:00
SmashingGrace wrote:
stolyar wrote:
Triangle ABC has sides 15, 17, and X. If X is an integer, then what are the greatest and the smallest possible X?

From triangle inequalities, we get 17 - 15 < x < 15 + 17, => 3 and 31, respectively, are minimum and maximum possible values of X.

Correct. BTW, how many X satisfy the question?

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Re: PS: ABC   [#permalink] 05 Jul 2004, 01:00
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