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

5, 2, 4
5, 2, 4

3, 3, 6
3, 3, 6

Answer 1

To determine which set of side lengths will form a triangle, we can use the triangle inequality theorem. According to this theorem, for three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's analyze each set of side lengths:

1. **8, 6, 2**
- 8 + 6 > 2 (True)
- 8 + 2 > 6 (True)
- 6 + 2 > 8 (False)
- This set does not form a triangle.

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

3. **5, 2, 4**
- 5 + 2 > 4 (True)
- 5 + 4 > 2 (True)
- 2 + 4 > 5 (True)
- This set forms a triangle.

4. **3, 3, 6**
- 3 + 3 > 6 (False)
- This set does not form a triangle.

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