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Which of the following cannot be the sides of any triangle?
- a)2, 12, 15
- b)5, 7, 11
- c)5, 12, 13
- d)3, 4, 5
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Which of the following cannot be the sides of any triangle?a)2, 12, 15...
2 + 12 < 15,
So, 2, 12, 15 cannot be sides of a triangle.
So, 2, 12, 15 cannot be sides of a triangle.
Most Upvoted Answer
Which of the following cannot be the sides of any triangle?a)2, 12, 15...
Understanding Triangle Inequality Theorem
To determine whether a set of three lengths can form a triangle, we apply the Triangle Inequality Theorem. This theorem states that for any three sides (a, b, c) of a triangle, the following conditions must hold true:
- a + b > c
- a + c > b
- b + c > a
If any of these conditions fail, the lengths cannot form a triangle.
Analysis of Option A: 2, 12, 15
Let's apply the Triangle Inequality Theorem to the sides 2, 12, and 15:
- Condition 1 (2 + 12 > 15):
- 14 > 15 (False)
- Condition 2 (2 + 15 > 12):
- 17 > 12 (True)
- Condition 3 (12 + 15 > 2):
- 27 > 2 (True)
Since the first condition is false, the lengths 2, 12, and 15 cannot form a triangle.
Analysis of Other Options
- Option B: 5, 7, 11:
- 5 + 7 > 11 (False; 12 > 11)
- 5 + 11 > 7 (True)
- 7 + 11 > 5 (True)
- All conditions are satisfied.
- Option C: 5, 12, 13:
- 5 + 12 > 13 (True)
- 5 + 13 > 12 (True)
- 12 + 13 > 5 (True)
- All conditions are satisfied.
- Option D: 3, 4, 5:
- 3 + 4 > 5 (True)
- 3 + 5 > 4 (True)
- 4 + 5 > 3 (True)
- All conditions are satisfied.
Conclusion
Thus, the only option that cannot be the sides of any triangle is option A: 2, 12, 15.
To determine whether a set of three lengths can form a triangle, we apply the Triangle Inequality Theorem. This theorem states that for any three sides (a, b, c) of a triangle, the following conditions must hold true:
- a + b > c
- a + c > b
- b + c > a
If any of these conditions fail, the lengths cannot form a triangle.
Analysis of Option A: 2, 12, 15
Let's apply the Triangle Inequality Theorem to the sides 2, 12, and 15:
- Condition 1 (2 + 12 > 15):
- 14 > 15 (False)
- Condition 2 (2 + 15 > 12):
- 17 > 12 (True)
- Condition 3 (12 + 15 > 2):
- 27 > 2 (True)
Since the first condition is false, the lengths 2, 12, and 15 cannot form a triangle.
Analysis of Other Options
- Option B: 5, 7, 11:
- 5 + 7 > 11 (False; 12 > 11)
- 5 + 11 > 7 (True)
- 7 + 11 > 5 (True)
- All conditions are satisfied.
- Option C: 5, 12, 13:
- 5 + 12 > 13 (True)
- 5 + 13 > 12 (True)
- 12 + 13 > 5 (True)
- All conditions are satisfied.
- Option D: 3, 4, 5:
- 3 + 4 > 5 (True)
- 3 + 5 > 4 (True)
- 4 + 5 > 3 (True)
- All conditions are satisfied.
Conclusion
Thus, the only option that cannot be the sides of any triangle is option A: 2, 12, 15.
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Which of the following cannot be the sides of any triangle?a)2, 12, 15b)5, 7, 11c)5, 12, 13d)3, 4, 5Correct answer is option 'A'. Can you explain this answer?
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