Question

Which set of side lengths will form a triangle? (1 point) Responses 4,1,6 4,1,6 3,4,6 3,4,6 5,2,3 5,2,3 8,6,2 8,6,2

Answer 1

To determine whether a set of side lengths can form a triangle, we can use the triangle inequality theorem. The theorem states that for any three lengths \(a\), \(b\), and \(c\), the following conditions must be met:

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

Let's analyze each set of side lengths provided:

1. **4, 1, 6**
- \(4 + 1 = 5\) (not > 6)
- Therefore, **cannot form a triangle**.

2. **3, 4, 6**
- \(3 + 4 = 7 > 6\)
- \(3 + 6 = 9 > 4\)
- \(4 + 6 = 10 > 3\)
- Therefore, **can form a triangle**.

3. **5, 2, 3**
- \(5 + 2 = 7 > 3\)
- \(5 + 3 = 8 > 2\)
- \(2 + 3 = 5\) (not > 5)
- Therefore, **cannot form a triangle**.

4. **8, 6, 2**
- \(8 + 6 = 14 > 2\)
- \(8 + 2 = 10 > 6\)
- \(6 + 2 = 8\) (not > 8)
- Therefore, **cannot form a triangle**.

Based on the analysis, only the set **3, 4, 6** can form a triangle.