Question

Apply the triangle inequaity theorem to determine which three sides lengths form a triangle. 8,8,20 8,4,12 20,10,30 10,20,15

Answer 1

In order for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.

1. For sides of lengths 8, 8, 20:
- 8 + 8 = 16 < 20. This does not satisfy the triangle inequality theorem and therefore these side lengths cannot form a triangle.

2. For sides of lengths 8, 4, 12:
- 8 + 4 = 12 > 12. This satisfies the triangle inequality theorem.
- 8 + 12 = 20 > 4. This satisfies the triangle inequality theorem.
- 4 + 12 = 16 > 8. This satisfies the triangle inequality theorem.
Therefore, sides of lengths 8, 4, and 12 form a triangle.

3. For sides of lengths 20, 10, 30:
- 20 + 10 = 30 > 30. This satisfies the triangle inequality theorem.
- 20 + 30 = 50 > 10. This satisfies the triangle inequality theorem.
- 10 + 30 = 40 > 20. This satisfies the triangle inequality theorem.
Therefore, sides of lengths 20, 10, and 30 form a triangle.

4. For sides of lengths 10, 20, 15:
- 10 + 20 = 30 > 15. This satisfies the triangle inequality theorem.
- 10 + 15 = 25 > 20. This satisfies the triangle inequality theorem.
- 20 + 15 = 35 > 10. This satisfies the triangle inequality theorem.
Therefore, sides of lengths 10, 20, and 15 form a triangle.