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A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.
- a)3 cm, 4 cm, 5 cm
- b)7 cm, 6 cm, 5 cm
- c)10 cm, 7 cm, 2 cm
- d)12 cm, 8 cm, 6 cm
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A Choose the correct option in which a triangle CANNOT be constructed ...
The difference of any two sides of a triangle must be less than the third side. This property of triangles is not satisfied by the given measurements as 10−7 = 3 > 2 and 10−2 = 8 > 7, though 7−2 = 5 < 10 is true.
Most Upvoted Answer
A Choose the correct option in which a triangle CANNOT be constructed ...
Explanation:
To determine if a triangle can be constructed with the given lengths of sides, 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
Now let's examine each option to see if a triangle can be constructed:
Option a) 3 cm, 4 cm, 5 cm:
- 3 + 4 > 5 (True)
- 4 + 5 > 3 (True)
- 3 + 5 > 4 (True)
All three conditions are satisfied, so a triangle can be constructed with these side lengths.
Option b) 7 cm, 6 cm, 5 cm:
- 7 + 6 > 5 (True)
- 6 + 5 > 7 (True)
- 7 + 5 > 6 (True)
All three conditions are satisfied, so a triangle can be constructed with these side lengths.
Option c) 10 cm, 7 cm, 2 cm:
- 10 + 7 > 2 (False)
The sum of the lengths of the two shorter sides (7 and 2) is not greater than the length of the longest side (10). Therefore, a triangle cannot be constructed with these side lengths.
Option d) 12 cm, 8 cm, 6 cm:
- 12 + 8 > 6 (True)
- 8 + 6 > 12 (False)
The sum of the lengths of the two shorter sides (8 and 6) is not greater than the length of the longest side (12). Therefore, a triangle cannot be constructed with these side lengths.
Conclusion:
Among the given options, the triangle cannot be constructed with the side lengths of 10 cm, 7 cm, and 2 cm (option c).
To determine if a triangle can be constructed with the given lengths of sides, 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
Now let's examine each option to see if a triangle can be constructed:
Option a) 3 cm, 4 cm, 5 cm:
- 3 + 4 > 5 (True)
- 4 + 5 > 3 (True)
- 3 + 5 > 4 (True)
All three conditions are satisfied, so a triangle can be constructed with these side lengths.
Option b) 7 cm, 6 cm, 5 cm:
- 7 + 6 > 5 (True)
- 6 + 5 > 7 (True)
- 7 + 5 > 6 (True)
All three conditions are satisfied, so a triangle can be constructed with these side lengths.
Option c) 10 cm, 7 cm, 2 cm:
- 10 + 7 > 2 (False)
The sum of the lengths of the two shorter sides (7 and 2) is not greater than the length of the longest side (10). Therefore, a triangle cannot be constructed with these side lengths.
Option d) 12 cm, 8 cm, 6 cm:
- 12 + 8 > 6 (True)
- 8 + 6 > 12 (False)
The sum of the lengths of the two shorter sides (8 and 6) is not greater than the length of the longest side (12). Therefore, a triangle cannot be constructed with these side lengths.
Conclusion:
Among the given options, the triangle cannot be constructed with the side lengths of 10 cm, 7 cm, and 2 cm (option c).
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A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer?
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A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer?.
A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? for Class 7 2025 is part of Class 7 preparation. The Question and answers have been prepared according to the Class 7 exam syllabus. Information about A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 7 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer?.
Solutions for A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 7.
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A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice A Choose the correct option in which a triangle CANNOT be constructed with the given lengths of sides.a)3 cm, 4 cm, 5 cmb)7 cm, 6 cm, 5 cmc)10 cm, 7 cm, 2 cmd)12 cm, 8 cm, 6 cmCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 7 tests.
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