Question

Which sets of side lengths form a triangle? All lengths are given in inches.
(Choose 3 answers.)
(1 point)
9, 17, 11
11, 19, 9
18, 10, 8
18, 11, 8

Answer 1

To determine if a set of side lengths can form a triangle, we can use the Triangle Inequality Theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must hold:

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

Let's evaluate each set of side lengths provided:

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

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

3. **18, 10, 8**:
- \(18 + 10 = 28 > 8\) (satisfied)
- \(18 + 8 = 26 > 10\) (satisfied)
- \(10 + 8 = 18\) (not satisfied)
- **This set cannot form a triangle.**

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

Based on these evaluations, the sets of side lengths that can form triangles are:

- **9, 17, 11**
- **11, 19, 9**
- **18, 11, 8**