Question

Which set of side lengths will form a triangle? All measurements are in feet.(1 point) Responses 8, 6, 2 8, 6, 2 3, 3, 6 3, 3, 6 5, 2, 4 5, 2, 4 4, 1, 6

Answer 1

To determine which set of side lengths can form a triangle, we can use the triangle inequality theorem. According to this theorem, for any three sides \(a\), \(b\), and \(c\), the following must be true:

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

We'll check each set of side lengths given:

1. **8, 6, 2**:
- \(8 + 6 > 2\) (14 > 2, true)
- \(8 + 2 > 6\) (10 > 6, true)
- \(6 + 2 > 8\) (8 > 8, false)
- **Does not form a triangle.**

2. **3, 3, 6**:
- \(3 + 3 > 6\) (6 > 6, false)
- **Does not form a triangle.**

3. **5, 2, 4**:
- \(5 + 2 > 4\) (7 > 4, true)
- \(5 + 4 > 2\) (9 > 2, true)
- \(2 + 4 > 5\) (6 > 5, true)
- **Forms a triangle.**

4. **4, 1, 6**:
- \(4 + 1 > 6\) (5 > 6, false)
- **Does not form a triangle.**

The only set of side lengths that will form a triangle is **5, 2, 4**.