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

help

Answer 1

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 side lengths \(a\), \(b\), and \(c\) (where \(a \leq b \leq c\)), the following conditions must hold:

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

Let's check each set of side lengths:

1. **18, 11, 8**
- \(11 + 8 = 19 > 18\) ✔️
- \(18 + 8 = 26 > 11\) ✔️
- \(18 + 11 = 29 > 8\) ✔️
- **Forms a triangle.**

2. **18, 10, 8**
- \(10 + 8 = 18 \not> 18\) ❌
- **Does not form a triangle.**
- \(18 + 8 = 26 > 10\) ✔️
- \(18 + 10 = 28 > 8\) ✔️

3. **11, 19, 9**
- \(11 + 9 = 20 > 19\) ✔️
- \(19 + 9 = 28 > 11\) ✔️
- \(19 + 11 = 30 > 9\) ✔️
- **Forms a triangle.**

4. **9, 17, 11**
- \(9 + 11 = 20 > 17\) ✔️
- \(17 + 11 = 28 > 9\) ✔️
- \(17 + 9 = 26 > 11\) ✔️
- **Forms a triangle.**

Based on the checks, the set of side lengths that does not form a triangle is:

**18, 10, 8**.