Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.
8, 4, 12
10, 20, 15
8, 8, 20
20, 10, 30
To determine which three side lengths form a triangle, we can apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
1. For the side lengths 8, 4, 12:
- 8 + 4 = 12 > 12 (not a triangle)
- 4 + 12 = 16 > 8
- 8 + 12 = 20 > 4
Therefore, the side lengths 4, 8, and 12 form a triangle.
2. For the side lengths 10, 20, 15:
- 10 + 20 = 30 > 15
- 20 + 15 = 35 > 10
- 10 + 15 = 25 > 20
Therefore, the side lengths 10, 20, and 15 form a triangle.
3. For the side lengths 8, 8, 20:
- 8 + 8 = 16 > 20 (not a triangle)
- 8 + 20 = 28 > 8
- 8 + 20 = 28 > 8
Therefore, the side lengths 8, 8, and 20 form a triangle.
4. For the side lengths 20, 10, 30:
- 20 + 10 = 30 > 30 (not a triangle)
- 10 + 30 = 40 > 20
- 20 + 30 = 50 > 10
Therefore, the side lengths 10, 20, and 30 do not form a triangle.