Question

Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point) Responses 18, 11, 8 18, 11, 8 18, 10, 8 18, 10, 8 11, 19, 9 11, 19, 9 9, 17, 11

Answer 1

To determine whether a set of side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for three sides \(a\), \(b\), and \(c\), the following inequalities must hold true:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Let's analyze each set of side lengths:

1. **18, 11, 8**
- \(18 + 11 = 29 > 8\) (True)
- \(18 + 8 = 26 > 11\) (True)
- \(11 + 8 = 19 > 18\) (True)

This set can form a triangle.

2. **18, 10, 8**
- \(18 + 10 = 28 > 8\) (True)
- \(18 + 8 = 26 > 10\) (True)
- \(10 + 8 = 18 \text{ is not greater than } 18\) (False)

This set cannot form a triangle.

3. **11, 19, 9**
- \(11 + 19 = 30 > 9\) (True)
- \(11 + 9 = 20 > 19\) (False)
- \(19 + 9 = 28 > 11\) (True)

This set cannot form a triangle.

4. **9, 17, 11**
- \(9 + 17 = 26 > 11\) (True)
- \(9 + 11 = 20 > 17\) (False)
- \(17 + 11 = 28 > 9\) (True)

This set cannot form a triangle.

Among these sets, **the side lengths 18, 10, 8 cannot form a triangle.**