Question

Which set of side lengths will form a triangle? All measurements are in feet.(1 point)
Responses

8, 6, 2
8, 6, 2

4, 1, 6
4, 1, 6

3, 3, 6
3, 3, 6

5, 2, 4
5, 2, 4

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 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. **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.

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

3. **3, 3, 6:**
- 3 + 3 > 6 (6 > 6) ✗
- This set does **not** form a triangle.

4. **5, 2, 4:**
- 5 + 2 > 4 (7 > 4) ✓
- 5 + 4 > 2 (9 > 2) ✓
- 2 + 4 > 5 (6 > 5) ✓
- This set **does** form a triangle.

Out of the given options, only the side lengths **5, 2, and 4** form a valid triangle.