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The construction of a triangle ABC with AB = 6 cm and ∠A = 600 is not possible when sum of BC and CA is equal to
- a)5.5 cm
- b)7 cm
- c)8 cm
- d)7.5 cm
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The construction of a triangle ABC with AB = 6 cm and∠A = 600 is n...
60+x+x=180
=2x=180-60
=2x=120
x=120/2
x=60
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The construction of a triangle ABC with AB = 6 cm and∠A = 600 is n...
Understanding Triangle Construction
To determine the possibility of constructing triangle ABC with given parameters, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
Given Parameters
- AB = 6 cm
- ∠A = 60°
- BC + CA = X (We need to evaluate various values for X)
Triangle Inequality Conditions
For triangle ABC, we derive the following conditions based on the sides:
1. AB + BC > CA
2. AB + CA > BC
3. BC + CA > AB
Given AB = 6 cm, we'll analyze the conditions when BC + CA = X.
Evaluating Each Option
- Option A: X = 5.5 cm
- BC + CA = 5.5 cm
- This implies BC + CA < ab="" (6="" cm).="" -="" therefore,="" at="" least="" one="" of="" the="" triangle="" inequalities="" fails,="" making="" triangle="" abc="" impossible.="" -="" />option="" b:="" x="7" cm="" -="" bc="" +="" ca="7" cm="" -="" this="" still="" satisfies="" ab="" +="" bc=""> CA, but does not necessarily violate the triangle inequality.
- Option C: X = 8 cm
- BC + CA = 8 cm
- This satisfies the triangle inequality, allowing for triangle construction.
- Option D: X = 7.5 cm
- Similar to option B and C, this value also satisfies the triangle inequality.
Conclusion
The only value that fails to meet the triangle inequality is 5.5 cm (Option A), making the construction of triangle ABC impossible in this case.
To determine the possibility of constructing triangle ABC with given parameters, we need to apply the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
Given Parameters
- AB = 6 cm
- ∠A = 60°
- BC + CA = X (We need to evaluate various values for X)
Triangle Inequality Conditions
For triangle ABC, we derive the following conditions based on the sides:
1. AB + BC > CA
2. AB + CA > BC
3. BC + CA > AB
Given AB = 6 cm, we'll analyze the conditions when BC + CA = X.
Evaluating Each Option
- Option A: X = 5.5 cm
- BC + CA = 5.5 cm
- This implies BC + CA < ab="" (6="" cm).="" -="" therefore,="" at="" least="" one="" of="" the="" triangle="" inequalities="" fails,="" making="" triangle="" abc="" impossible.="" -="" />option="" b:="" x="7" cm="" -="" bc="" +="" ca="7" cm="" -="" this="" still="" satisfies="" ab="" +="" bc=""> CA, but does not necessarily violate the triangle inequality.
- Option C: X = 8 cm
- BC + CA = 8 cm
- This satisfies the triangle inequality, allowing for triangle construction.
- Option D: X = 7.5 cm
- Similar to option B and C, this value also satisfies the triangle inequality.
Conclusion
The only value that fails to meet the triangle inequality is 5.5 cm (Option A), making the construction of triangle ABC impossible in this case.
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The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer?.
The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer? for Class 9 2026 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 9 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The construction of a triangle ABC with AB = 6 cm and∠A = 600 is not possible when sum of BC and CA is equal toa)5.5 cmb)7 cmc)8 cmd)7.5 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 9.
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