Question

Which set of side lengths will form a triangle? (1 point)
Responses

5,2,3
5,2,3

4,1,6
4,1,6

3,4,6
3,4,6

8,6,2

Answer 1

To determine which set of side lengths can form a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's evaluate each set of side lengths:

1. **5, 2, 3**:
- 5 + 2 > 3 (7 > 3) ✔️
- 5 + 3 > 2 (8 > 2) ✔️
- 2 + 3 > 5 (5 > 5) ❌
- This set does not form a triangle.

2. **4, 1, 6**:
- 4 + 1 > 6 (5 > 6) ❌
- This set does not form a triangle.

3. **3, 4, 6**:
- 3 + 4 > 6 (7 > 6) ✔️
- 3 + 6 > 4 (9 > 4) ✔️
- 4 + 6 > 3 (10 > 3) ✔️
- This set forms a triangle.

4. **8, 6, 2**:
- 8 + 6 > 2 (14 > 2) ✔️
- 8 + 2 > 6 (10 > 6) ✔️
- 6 + 2 > 8 (8 > 8) ❌
- This set does not form a triangle.

Based on the checks above, the only set of side lengths that can form a triangle is **3, 4, 6**.