Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)
Responses
8, 4, 12
8, 4, 12
10, 20, 15
10, 20, 15
8, 8, 20
8, 8, 20
20, 10, 30
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Using this theorem:
1. For the sides 8, 4, 12:
- 8 + 4 = 12, which is greater than 12 (third side)
- 8 + 12 = 20, which is greater than 4 (third side)
- 4 + 12 = 16, which is greater than 8 (third side)
Therefore, 8, 4, 12 can form a triangle.
2. For the sides 10, 20, 15:
- 10 + 20 = 30, which is greater than 15 (third side)
- 10 + 15 = 25, which is greater than 20 (third side)
- 20 + 15 = 35, which is not greater than 10 (third side)
Therefore, 10, 20, 15 cannot form a triangle.
3. For the sides 8, 8, 20:
- 8 + 8 = 16, which is greater than 20 (third side)
- 8 + 20 = 28, which is greater than 8 (third side)
- 8 + 20 = 28, which is greater than 8 (third side)
Therefore, 8, 8, 20 can form a triangle.
4. For the sides 20, 10, 30:
- 20 + 10 = 30, which is not greater than 30 (third side)
- 20 + 30 = 50, which is greater than 10 (third side)
- 10 + 30 = 40, which is greater than 20 (third side)
Therefore, 20, 10, 30 cannot form a triangle.
The three side lengths that form a triangle are:
- 8, 4, 12
- 8, 8, 20