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# A triangle has sides 12, 6, and z. Which of the following cannot be th

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Math Expert
Joined: 02 Sep 2009
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A triangle has sides 12, 6, and z. Which of the following cannot be th  [#permalink]

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02 Sep 2018, 20:55
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Difficulty:

15% (low)

Question Stats:

83% (00:58) correct 17% (01:03) wrong based on 32 sessions

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A triangle has sides 12, 6, and z. Which of the following cannot be the perimeter of the triangle?

A. 24
B. 28
C. 30
D. 35
E. 35.5

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Joined: 10 Jan 2013
Posts: 171
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Concentration: General Management, Strategy
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Re: A triangle has sides 12, 6, and z. Which of the following cannot be th  [#permalink]

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02 Sep 2018, 22:11
Not sure but the property is that the third side x will follow this

6 < x < 18

x can be 7,8,9....17

So bcd are out.

Confused between A and E

Posted from my mobile device
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Joined: 08 Oct 2015
Posts: 241
Re: A triangle has sides 12, 6, and z. Which of the following cannot be th  [#permalink]

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02 Sep 2018, 22:14
saurabh9gupta wrote:
Not sure but the property is that the third side x will follow this

6 < x < 18

x can be 7,8,9....17

So bcd are out.

Confused between A and E

Posted from my mobile device

x can be any number greater than 6, and not just integers.
Hence x can b 6.00001 or 17.999
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Re: A triangle has sides 12, 6, and z. Which of the following cannot be th  [#permalink]

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03 Sep 2018, 07:39
1
Bunuel wrote:
A triangle has sides 12, 6, and z. Which of the following cannot be the perimeter of the triangle?

A. 24
B. 28
C. 30
D. 35
E. 35.5

$$6 < 3^{rd} Side < 18$$

So, The range of perimeter must be $$24 < Perimeter < 36$$

Hence, Answer must be (A) 24
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Re: A triangle has sides 12, 6, and z. Which of the following cannot be th  [#permalink]

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11 Sep 2018, 16:12
Bunuel wrote:
A triangle has sides 12, 6, and z. Which of the following cannot be the perimeter of the triangle?

A. 24
B. 28
C. 30
D. 35
E. 35.5

The two sides 12 and 6 sum to 18. Since the sum of any 2 sides of a triangle must be greater than the third, we see that the third side of the triangle must be greater than 6, and thus the perimeter must be greater than 24. So 24 can’t be the perimeter of the triangle.

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Re: A triangle has sides 12, 6, and z. Which of the following cannot be th   [#permalink] 11 Sep 2018, 16:12
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