To determine if three side lengths can form a triangle, we can use the triangle inequality theorem. According to this theorem, for three sides \(a\), \(b\), and \(c\) to form a triangle, the following conditions must be met:
- \(a + b > c\)
- \(a + c > b\)
- \(b + c > a\)
Now, let's evaluate each set of side lengths provided:
-
3, 3, 6
- \(3 + 3 > 6\) → False
- This set does not form a triangle.
-
5, 2, 4
- \(5 + 2 > 4\) → True (7 > 4)
- \(5 + 4 > 2\) → True (9 > 2)
- \(2 + 4 > 5\) → True (6 > 5)
- This set forms a triangle.
-
8, 6, 2
- \(8 + 6 > 2\) → True (14 > 2)
- \(8 + 2 > 6\) → True (10 > 6)
- \(6 + 2 > 8\) → False (8 is not greater than 8)
- This set does not form a triangle.
-
4, 1, 6
- \(4 + 1 > 6\) → False (5 is not greater than 6)
- This set does not form a triangle.
Based on this analysis, the only set of side lengths that can form a triangle is 5, 2, 4.