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The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ?
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The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is ...
To determine the minimum value that side "a" can take in a triangle with sides measuring 10 cm and 6.5 cm, we will apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
Triangle Inequality Conditions
For the sides of the triangle (10 cm, 6.5 cm, and a), the following conditions must hold true:
- **Condition 1**: 10 + 6.5 > a
- This simplifies to:
a < 16.5="" />
- **Condition 2**: 10 + a > 6.5
- This simplifies to:
a > -3.5 (which is always true since a is a whole number)
- **Condition 3**: 6.5 + a > 10
- This simplifies to:
a > 3.5
Calculating Minimum Value of "a"
Since "a" must be a whole number, we need to find the smallest whole number greater than 3.5. Therefore, the minimum value of "a" is:
- **Minimum value of "a"**: 4
Conclusion
To summarize, the smallest whole number that satisfies the triangle inequality conditions for the sides measuring 10 cm, 6.5 cm, and "a" is:
- **Final Answer**: a = 4
Triangle Inequality Conditions
For the sides of the triangle (10 cm, 6.5 cm, and a), the following conditions must hold true:
- **Condition 1**: 10 + 6.5 > a
- This simplifies to:
a < 16.5="" />
- **Condition 2**: 10 + a > 6.5
- This simplifies to:
a > -3.5 (which is always true since a is a whole number)
- **Condition 3**: 6.5 + a > 10
- This simplifies to:
a > 3.5
Calculating Minimum Value of "a"
Since "a" must be a whole number, we need to find the smallest whole number greater than 3.5. Therefore, the minimum value of "a" is:
- **Minimum value of "a"**: 4
Conclusion
To summarize, the smallest whole number that satisfies the triangle inequality conditions for the sides measuring 10 cm, 6.5 cm, and "a" is:
- **Final Answer**: a = 4
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The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ?
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The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ?.
The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sides of a triangle have lengths 10 cm, 6.5 cm and a , where a is a whole number. The minimum value that a can take is ?.
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