Which set of side lengths will form a triangle? All measurements are in feet.(1 point) Responses 3, 3, 6 3, 3, 6 5, 2, 4 5, 2, 4 8, 6, 2 8, 6, 2 4, 1, 6

Answer 1

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:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

Now, let's evaluate each set of side lengths provided:

1. 3, 3, 6

   • \(3 + 3 > 6\) → False
   • This set does not form a triangle.

2. 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.

3. 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. 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.