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Which of the following triplets does not represent the sides of a triangle?
- a)(3, 4, 5)
- b)(4, 7, 10)
- c)(3, 6, 8)
- d)(2, 3, 6)
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Which of the following triplets does not represent the sides of a tria...
Following condition is must in any triangle∶
(Sum of 2 sides) > Third Side
In option 4∶ (2, 3, 6)
(2 + 3) < 6
(Sum of 2 sides) > Third Side
In option 4∶ (2, 3, 6)
(2 + 3) < 6
That means it does not fulfil the necessary condition.
∴ Triplets (2, 3, 6) does not represent the sides of a triangle.
∴ Triplets (2, 3, 6) does not represent the sides of a triangle.
Most Upvoted Answer
Which of the following triplets does not represent the sides of a tria...
Explanation:
To determine whether a given set of numbers can form the sides of a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Triangle Inequality Theorem:
For a triangle with sides of lengths a, b, and c:
a + b > c
b + c > a
a + c > b
Let's analyze each option to see if it satisfies the triangle inequality theorem:
a) (3, 4, 5):
In this case, 3 + 4 > 5 (7 > 5), 4 + 5 > 3 (9 > 3), and 3 + 5 > 4 (8 > 4). Therefore, this option represents a valid triangle.
b) (4, 7, 10):
For this option, 4 + 7 > 10 (11 > 10), 7 + 10 > 4 (17 > 4), and 4 + 10 > 7 (14 > 7). So, this option represents a valid triangle as well.
c) (3, 6, 8):
Applying the triangle inequality theorem, we can see that 3 + 6 > 8 (9 > 8), 6 + 8 > 3 (14 > 3), and 3 + 8 > 6 (11 > 6). Therefore, this option also represents a valid triangle.
d) (2, 3, 6):
In this case, we have 2 + 3 > 6 (5 > 6), 3 + 6 > 2 (9 > 2), but 2 + 6 is not greater than 3 (8 is not greater than 3). Thus, this option does not satisfy the triangle inequality theorem and does not represent a valid triangle.
Therefore, the correct answer is option 'D' - (2, 3, 6) does not represent the sides of a triangle.
To determine whether a given set of numbers can form the sides of a triangle, we need to apply the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Triangle Inequality Theorem:
For a triangle with sides of lengths a, b, and c:
a + b > c
b + c > a
a + c > b
Let's analyze each option to see if it satisfies the triangle inequality theorem:
a) (3, 4, 5):
In this case, 3 + 4 > 5 (7 > 5), 4 + 5 > 3 (9 > 3), and 3 + 5 > 4 (8 > 4). Therefore, this option represents a valid triangle.
b) (4, 7, 10):
For this option, 4 + 7 > 10 (11 > 10), 7 + 10 > 4 (17 > 4), and 4 + 10 > 7 (14 > 7). So, this option represents a valid triangle as well.
c) (3, 6, 8):
Applying the triangle inequality theorem, we can see that 3 + 6 > 8 (9 > 8), 6 + 8 > 3 (14 > 3), and 3 + 8 > 6 (11 > 6). Therefore, this option also represents a valid triangle.
d) (2, 3, 6):
In this case, we have 2 + 3 > 6 (5 > 6), 3 + 6 > 2 (9 > 2), but 2 + 6 is not greater than 3 (8 is not greater than 3). Thus, this option does not satisfy the triangle inequality theorem and does not represent a valid triangle.
Therefore, the correct answer is option 'D' - (2, 3, 6) does not represent the sides of a triangle.
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Which of the following triplets does not represent the sides of a triangle?a)(3, 4, 5)b)(4, 7, 10)c)(3, 6, 8)d)(2, 3, 6)Correct answer is option 'D'. Can you explain this answer?
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