Question

Which set of side lengths does not form a triangle? All lengths are given in inches. (1 point)

Ο 9, 17, 11

Ο 11, 19,9

Ο 18, 10, 8

18, 11,8

Answer 1

To determine which set of side lengths does not form a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\):

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

We will check each set of lengths:

1. **For 9, 17, 11**:
- \(9 + 11 = 20 > 17\) (True)
- \(9 + 17 = 26 > 11\) (True)
- \(11 + 17 = 28 > 9\) (True)
- **This set can form a triangle.**

2. **For 11, 19, 9**:
- \(11 + 9 = 20 > 19\) (True)
- \(11 + 19 = 30 > 9\) (True)
- \(9 + 19 = 28 > 11\) (True)
- **This set can form a triangle.**

3. **For 18, 10, 8**:
- \(18 + 10 = 28 > 8\) (True)
- \(18 + 8 = 26 > 10\) (True)
- \(10 + 8 = 18 > 18\) (False)
- **This set does NOT form a triangle.**

4. **For 18, 11, 8**:
- \(18 + 11 = 29 > 8\) (True)
- \(18 + 8 = 26 > 11\) (True)
- \(11 + 8 = 19 > 18\) (True)
- **This set can form a triangle.**

Thus, the set of side lengths that does not form a triangle is **18, 10, 8**.