Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
8, 4, 12
8, 4, 12
8, 8, 20
8, 8, 20
10, 20, 15
10, 20, 15
20, 10, 30
To determine which three side lengths form a triangle, we 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.
Let's apply this to the given side lengths:
1. For the side lengths 8, 4, 12:
- 8 + 4 = 12, which is greater than 12
- 4 + 12 = 16, which is greater than 8
- 8 + 12 = 20, which is greater than 4
Therefore, the side lengths 8, 4, 12 form a triangle.
2. For the side lengths 8, 8, 20:
- 8 + 8 = 16, which is not greater than 20
- 8 + 20 = 28, which is greater than 8
- 8 + 20 = 28, which is greater than 8
Therefore, the side lengths 8, 8, 20 do not form a triangle.
3. For the side lengths 10, 20, 15:
- 10 + 20 = 30, which is greater than 15
- 10 + 15 = 25, which is greater than 20
- 20 + 15 = 35, which is greater than 10
Therefore, the side lengths 10, 20, 15 form a triangle.
4. For the side lengths 20, 10, 30:
- 20 + 10 = 30, which is greater than 30
- 20 + 30 = 50, which is greater than 10
- 10 + 30 = 40, which is greater than 20
Therefore, the side lengths 20, 10, 30 form a triangle.