To determine which set of side lengths does not form a triangle, we can use the Triangle Inequality Theorem. According to this theorem, for any three lengths \(a\), \(b\), and \(c\), they can form a triangle if the following conditions hold:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
Let's apply this to each set of lengths:
-
11, 19, 9:
- \(11 + 19 = 30 > 9\) (True)
- \(11 + 9 = 20 > 19\) (True)
- \(19 + 9 = 28 > 11\) (True)
This set can form a triangle.
-
18, 11, 8:
- \(18 + 11 = 29 > 8\) (True)
- \(18 + 8 = 26 > 11\) (True)
- \(11 + 8 = 19 > 18\) (True)
This set can form a triangle.
-
18, 10, 8:
- \(18 + 10 = 28 > 8\) (True)
- \(18 + 8 = 26 > 10\) (True)
- \(10 + 8 = 18\) (Not Greater)
This set does not satisfy the triangle inequality because \(10 + 8\) is not greater than \(18\).
-
9, 17, 11:
- \(9 + 17 = 26 > 11\) (True)
- \(9 + 11 = 20 > 17\) (True)
- \(17 + 11 = 28 > 9\) (True)
This set can form a triangle.
Conclusion: The set of side lengths that does not form a triangle is 18, 10, 8.