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If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number?
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If the side of an acute angle triangle are 10,14 and x find the total ...
Analysis of the Triangle:
- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Given sides of the triangle are 10, 14, and x.
- For x to be a part of a valid triangle, the sum of any two sides must be greater than x.
Possible Values of x:
- The possible combinations of sides that satisfy the triangle inequality are:
- 10 + 14 > x
- 14 + x > 10
- 10 + x > 14
- From the first inequality:
- 24 > x
- From the second inequality:
- 14 + x > 10
- x > -4 (Since x is a natural number)
- From the third inequality:
- 10 + x > 14
- x > 4
Combining the Inequalities:
- Combining the inequalities, we get:
- 24 > x > 4
Finding the Number of Possible Values of x:
- The natural numbers between 4 and 24 are:
- 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
- Therefore, there are 19 possible values of x that satisfy the conditions and form a valid triangle with sides of lengths 10, 14, and x.
- The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Given sides of the triangle are 10, 14, and x.
- For x to be a part of a valid triangle, the sum of any two sides must be greater than x.
Possible Values of x:
- The possible combinations of sides that satisfy the triangle inequality are:
- 10 + 14 > x
- 14 + x > 10
- 10 + x > 14
- From the first inequality:
- 24 > x
- From the second inequality:
- 14 + x > 10
- x > -4 (Since x is a natural number)
- From the third inequality:
- 10 + x > 14
- x > 4
Combining the Inequalities:
- Combining the inequalities, we get:
- 24 > x > 4
Finding the Number of Possible Values of x:
- The natural numbers between 4 and 24 are:
- 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23
- Therefore, there are 19 possible values of x that satisfy the conditions and form a valid triangle with sides of lengths 10, 14, and x.
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If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number?
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If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number?.
If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the side of an acute angle triangle are 10,14 and x find the total number of possible value of x where x is a natural number?.
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