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# In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following c

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Math Expert
Joined: 02 Sep 2009
Posts: 55668
In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following c  [#permalink]

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11 Jan 2019, 00:38
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Difficulty:

15% (low)

Question Stats:

86% (00:51) correct 14% (01:05) wrong based on 25 sessions

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In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following cannot be a value of x?

A. 6
B. 7
C. 8
D. 9
E. 10

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Joined: 10 Feb 2018
Posts: 33
GMAT 1: 550 Q46 V20
Re: In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following c  [#permalink]

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11 Jan 2019, 01:06

The sum of lengths of any two sides of a triangle is greater than the length of the third side!

Here 6+6=12 is not greater than 12

Hence 6 cannot be the third side of the triangle.
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Re: In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following c  [#permalink]

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11 Jan 2019, 03:08
Bunuel wrote:
In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following cannot be a value of x?

A. 6
B. 7
C. 8
D. 9
E. 10

sum of two sides of triangle has to be greater than 3rd side
in this case option A 6 is right answer as all other options give side >12

IMO A
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Joined: 15 Feb 2018
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Re: In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following c  [#permalink]

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17 Jan 2019, 20:59
This question is about the triangle inequality theorem.

The 3rd side of a triangle must be greater than the difference of the other two sides, and must be less than the sum of the other two sides.

BC-AB<AC<BC+AB
12-6<AC<12+6
6<AC<18

Note, the above are < NOT ≤

Only 6 is not in the range.

A
Re: In triangle ABC, AB = 6, BC = 12, and AC = x. Which of the following c   [#permalink] 17 Jan 2019, 20:59
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