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# Which of the following measures could form the sides of a triangle?

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Math Expert
Joined: 02 Sep 2009
Posts: 60646
Which of the following measures could form the sides of a triangle?  [#permalink]

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29 Oct 2018, 04:27
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Difficulty:

25% (medium)

Question Stats:

74% (00:37) correct 26% (00:52) wrong based on 47 sessions

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Which of the following measures could form the sides of a triangle?

I) 3, 3, 5
II) 6, 6, 12
III) 1, 2, 3

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

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Re: Which of the following measures could form the sides of a triangle?  [#permalink]

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29 Oct 2018, 04:30
Which of the following measures could form the sides of a triangle?

I) 3, 3, 5
II) 6, 6, 12
III) 1, 2, 3

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.

Only option 1 goes right
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Re: Which of the following measures could form the sides of a triangle?  [#permalink]

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29 Oct 2018, 06:12
Bunuel wrote:
Which of the following measures could form the sides of a triangle?

I) 3, 3, 5
II) 6, 6, 12
III) 1, 2, 3

A. I only
B. II only
C. III only
D. I and II only
E. II and III only

Property: Property of a triangle states that sum of any two sides must be greater than the third side for a triangle to exist

I) 3, 3, 5 i.e. 3+3 > 5 i.e. Possible triangle
II) 6, 6, 12 i.e. 6+6 = 12 and NOT greater than 12 i.e. NO such triangle is possible
III) 1, 2, 3 i.e. 1+2 = 3 and NOT greater than 3 i.e. NO such triangle is possible

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Which of the following measures could form the sides of a triangle?  [#permalink]

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30 Oct 2018, 03:37

Solution

To find:
• Which among the given answer choices can be the side lengths of a triangle

Approach and Working:
• We know that, in a triangle,
o Sum of any two sides is greater than the third side
o Difference between any two sides is less than the third side
I) 3, 3, 5
3 + 3 > 5
3 + 5 > 3
3 – 3 < 5
5 – 3 < 3
Thus (I) can be the sides of a triangle

II) 6, 6, 12
6 + 6 = 12
Thus (II) cannot be the sides of a triangle

III) 1, 2, 3
1 + 2 = 3
Thus (III) cannot be the sides of a triangle

Hence, the correct answer is Option A

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Which of the following measures could form the sides of a triangle?   [#permalink] 30 Oct 2018, 03:37
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