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The length of two sides of a triangle are 4 and 6
column A - length of the third side
column B - 10
options
A-a is greater
B-b is greater
C-both are equal
D- can't not be determined without future information.?
column A - length of the third side
column B - 10
options
A-a is greater
B-b is greater
C-both are equal
D- can't not be determined without future information.?
Most Upvoted Answer
The length of two sides of a triangle are 4 and 6column A - length of ...
Understanding Triangle Inequality Theorem
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Given Sides
- Length of Side A = 4
- Length of Side B = 6
Third Side Length Calculation
To determine the possible lengths of the third side (let's call it C), we apply the triangle inequality theorem:
1. First Condition: A + B > C
- 4 + 6 > C
- C < />
2. Second Condition: A + C > B
- 4 + C > 6
- C > 2
3. Third Condition: B + C > A
- 6 + C > 4
- C > -2 (this condition is always true as C must be positive)
Conclusion on the Third Side Length
From the calculations above, we have:
- 2 < c="" />< />
This indicates that the length of the third side can be any value greater than 2 and less than 10.
Comparing with Column B
- Column A (possible range for C): 2 < c="" />< />
- Column B: 10
Final Determination
Since the length of the third side cannot equal or exceed 10, the comparison leads us to conclude:
- Column A is always less than Column B.
Thus, the answer is Option B: b is greater.
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Given Sides
- Length of Side A = 4
- Length of Side B = 6
Third Side Length Calculation
To determine the possible lengths of the third side (let's call it C), we apply the triangle inequality theorem:
1. First Condition: A + B > C
- 4 + 6 > C
- C < />
2. Second Condition: A + C > B
- 4 + C > 6
- C > 2
3. Third Condition: B + C > A
- 6 + C > 4
- C > -2 (this condition is always true as C must be positive)
Conclusion on the Third Side Length
From the calculations above, we have:
- 2 < c="" />< />
This indicates that the length of the third side can be any value greater than 2 and less than 10.
Comparing with Column B
- Column A (possible range for C): 2 < c="" />< />
- Column B: 10
Final Determination
Since the length of the third side cannot equal or exceed 10, the comparison leads us to conclude:
- Column A is always less than Column B.
Thus, the answer is Option B: b is greater.
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The length of two sides of a triangle are 4 and 6column A - length of the third side column B - 10 options A-a is greater B-b is greater C-both are equal D- can't not be determined without future information.?
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The length of two sides of a triangle are 4 and 6column A - length of the third side column B - 10 options A-a is greater B-b is greater C-both are equal D- can't not be determined without future information.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The length of two sides of a triangle are 4 and 6column A - length of the third side column B - 10 options A-a is greater B-b is greater C-both are equal D- can't not be determined without future information.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The length of two sides of a triangle are 4 and 6column A - length of the third side column B - 10 options A-a is greater B-b is greater C-both are equal D- can't not be determined without future information.?.
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