Grade 9 Exam > Grade 9 Questions > The construction ofABC, given that BC = 5 cm,...
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The construction of △ABC, given that BC = 5 cm, ∠B = 600 is not possible when the difference of AB and AC is equal to
- a)4.2 cm
- b)5.9 cm.
- c)4 cm.
- d)3 cm.
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The construction ofABC, given that BC = 5 cm,∠B = 600 is not possi...
Understanding the Problem
To construct triangle ABC with given conditions:
- BC = 5 cm
- ∠B = 60°
The construction is not possible when the difference of sides AB and AC is equal to specific values.
Triangle Inequality Theorem
For any triangle, the following inequalities must hold true:
1. AB + AC > BC
2. AB + BC > AC
3. AC + BC > AB
In this case, since BC = 5 cm, we need to consider the difference between sides AB and AC.
Difference of Sides
Let:
- AB = x cm
- AC = y cm
The condition can be expressed as |x - y| = d, where d is the difference. For the triangle to be valid, we analyze:
- If x - y = d, then:
- x = y + d
- If y - x = d, then:
- y = x + d
Substituting in the triangle inequalities leads to conditions for d.
Determining Non-Constructibility
To find the value of d for which the triangle cannot be constructed:
1. From the first inequality (AB + AC > BC):
- (x + y) > 5
2. From the second inequality:
- x + 5 > y → x > y - 5
- y + 5 > x → y > x - 5
3. The critical point occurs when |x - y| is maximized.
Calculating for Given Options
- For d = 5.9 cm, the condition becomes:
- If AB = 5.9 + AC, then:
- AB + AC = 5.9 + 2AC cannot exceed 5, violating the triangle inequality.
Thus, option b (5.9 cm) is the critical difference where construction fails.
Conclusion
In summary, the construction of triangle ABC is not possible when the difference between AB and AC is 5.9 cm.
To construct triangle ABC with given conditions:
- BC = 5 cm
- ∠B = 60°
The construction is not possible when the difference of sides AB and AC is equal to specific values.
Triangle Inequality Theorem
For any triangle, the following inequalities must hold true:
1. AB + AC > BC
2. AB + BC > AC
3. AC + BC > AB
In this case, since BC = 5 cm, we need to consider the difference between sides AB and AC.
Difference of Sides
Let:
- AB = x cm
- AC = y cm
The condition can be expressed as |x - y| = d, where d is the difference. For the triangle to be valid, we analyze:
- If x - y = d, then:
- x = y + d
- If y - x = d, then:
- y = x + d
Substituting in the triangle inequalities leads to conditions for d.
Determining Non-Constructibility
To find the value of d for which the triangle cannot be constructed:
1. From the first inequality (AB + AC > BC):
- (x + y) > 5
2. From the second inequality:
- x + 5 > y → x > y - 5
- y + 5 > x → y > x - 5
3. The critical point occurs when |x - y| is maximized.
Calculating for Given Options
- For d = 5.9 cm, the condition becomes:
- If AB = 5.9 + AC, then:
- AB + AC = 5.9 + 2AC cannot exceed 5, violating the triangle inequality.
Thus, option b (5.9 cm) is the critical difference where construction fails.
Conclusion
In summary, the construction of triangle ABC is not possible when the difference between AB and AC is 5.9 cm.
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The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer? for Grade 9 2025 is part of Grade 9 preparation. The Question and answers have been prepared according to the Grade 9 exam syllabus. Information about The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Grade 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer?.
The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer? for Grade 9 2025 is part of Grade 9 preparation. The Question and answers have been prepared according to the Grade 9 exam syllabus. Information about The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Grade 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer?.
Solutions for The construction ofABC, given that BC = 5 cm,∠B = 600 is not possible when the difference of AB and AC is equal toa)4.2 cmb)5.9 cm.c)4 cm.d)3 cm.Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Grade 9.
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