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:
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8, 6, 2
- 8 + 6 > 2 (True)
- 8 + 2 > 6 (True)
- 6 + 2 > 8 (False)
- This set does not form a triangle.
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4, 1, 6
- 4 + 1 > 6 (False)
- This set does not form a triangle.
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5, 2, 4
- 5 + 2 > 4 (True)
- 5 + 4 > 2 (True)
- 2 + 4 > 5 (True)
- This set forms a triangle.
-
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.