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The construction of a triangle ABC, given that BC = 3 cm, ∠C = 600 is possible when the difference of AB and AC is equal to
- a)2.8 cm.
- b)3 cm.
- c)3.1 cm.
- d)3.2 cm.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The construction of a triangle ABC, given that BC = 3 cm,∠C = 600 ...
Understanding the Triangle Construction
To determine the possible values for the sides AB and AC of triangle ABC, given the following conditions:
- BC = 3 cm
- ∠C = 60°
We will apply the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Applying Triangle Inequality
Let:
- AB = a
- AC = b
From the triangle inequality, we have:
1. **a + b > 3** (Equation 1)
2. **a + 3 > b** (Equation 2)
3. **b + 3 > a** (Equation 3)
Expressing the Difference
We also need to consider the difference between sides AB and AC:
- |a - b| = k (where k is the difference we are looking for)
This translates into two inequalities:
- a - b = k (or)
- b - a = k
Using these expressions, we can derive two scenarios for the difference:
Finding the Difference
1. **From Equation 1** (a + b > 3):
- For a - b = k:
- Substitute a = b + k into a + b > 3:
- (b + k) + b > 3 → 2b + k > 3 → 2b > 3 - k → b > (3 - k)/2
2. **From Equation 3** (b + 3 > a):
- Substitute a = b + k:
- b + 3 > (b + k) → 3 > k → k < />
Thus, the maximum difference can be 3 cm.
Finding the Specific Value
To find the exact value of the difference that satisfies all conditions, we can derive that the possible difference |a - b| must equal 2.8 cm allows for the triangle to form. Hence, the answer is option (a) 2.8 cm.
This analysis leads us to conclude that the difference of AB and AC must be exactly 2.8 cm for triangle ABC to be constructible under the given conditions.
To determine the possible values for the sides AB and AC of triangle ABC, given the following conditions:
- BC = 3 cm
- ∠C = 60°
We will apply the triangle inequality theorem, which states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Applying Triangle Inequality
Let:
- AB = a
- AC = b
From the triangle inequality, we have:
1. **a + b > 3** (Equation 1)
2. **a + 3 > b** (Equation 2)
3. **b + 3 > a** (Equation 3)
Expressing the Difference
We also need to consider the difference between sides AB and AC:
- |a - b| = k (where k is the difference we are looking for)
This translates into two inequalities:
- a - b = k (or)
- b - a = k
Using these expressions, we can derive two scenarios for the difference:
Finding the Difference
1. **From Equation 1** (a + b > 3):
- For a - b = k:
- Substitute a = b + k into a + b > 3:
- (b + k) + b > 3 → 2b + k > 3 → 2b > 3 - k → b > (3 - k)/2
2. **From Equation 3** (b + 3 > a):
- Substitute a = b + k:
- b + 3 > (b + k) → 3 > k → k < />
Thus, the maximum difference can be 3 cm.
Finding the Specific Value
To find the exact value of the difference that satisfies all conditions, we can derive that the possible difference |a - b| must equal 2.8 cm allows for the triangle to form. Hence, the answer is option (a) 2.8 cm.
This analysis leads us to conclude that the difference of AB and AC must be exactly 2.8 cm for triangle ABC to be constructible under the given conditions.
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The construction of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. 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 of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. 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 of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. Can you explain this answer?.
The construction of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. 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 of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. 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 of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. Can you explain this answer?.
Solutions for The construction of a triangle ABC, given that BC = 3 cm,∠C = 600 is possible when the difference of AB and AC is equal toa)2.8 cm.b)3 cm.c)3.1 cm.d)3.2 cm.Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Grade 9.
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