Final answer:
Among the provided options, the set of lengths 11, 19, 9 cannot form a triangle as it does not adhere to the triangle inequality theorem. Therefore, the correct option is C.
Step-by-step explanation:
The question pertains to the property of triangles which states that 'The sum of the lengths of any two sides of a triangle must be greater than the length of the third side'. This is known as the triangle inequality theorem. According to this theorem, any set of lengths that doesn't fulfill this condition cannot form a triangle.
Let's check the given sets of lengths:
- A. 18, 11, 8: 18 + 11 > 8 and 18 + 8 > 11 and 11 + 8 > 18 so, these sides can form a triangle.
- B. 9, 17, 11: 9 + 17 > 11 and 9 + 11 > 17 and 17 + 11 > 9 so, these sides can form a triangle.
- C. 11, 19, 9: 11 + 19 > 9 but 11 + 9 is not greater than 19 so, these lengths cannot form a triangle, violating the triangle inequality theorem.
- D. 18, 10, 8: 18 + 10 > 8 and 18 + 8 > 10 and 10 + 8 > 18 so, these sides can form a triangle.
Therefore, option C (11,19,9) does not form a triangle.
Learn more about Triangle Inequality Theorem