The side lengths of a triangle are 8, 17, and x units.178x(The figure above gives only one possible configuration for the triangle.)Determine the possible values of x.Write your answer as an inequality.Use x only once in your inequality.
Question
The side lengths of a triangle are 8, 17, and x units.178x(The figure above gives only one possible configuration for the triangle.)Determine the possible values of x.Write your answer as an inequality.Use x only once in your inequality.
Solution
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, for the given triangle, we have three inequalities:
- 8 + 17 > x
- 8 + x > 17
- 17 + x > 8
Solving these inequalities:
- 25 > x
- x > 9
- This inequality is always true since x is a positive number.
So, combining the first two inequalities, we get the possible values of x as 9 < x < 25.
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