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.
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