Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point) Responses 10, 20, 15 10, 20, 15 8, 4, 12 8, 4, 12 8, 8, 20 8, 8, 20 20, 10, 30

Answer 1

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.

Therefore, using the given sets of side lengths:

1) 10, 20, 15:
- 10 + 15 > 20 (25 > 20)
- 10 + 20 > 15 (30 > 15)
- 15 + 20 > 10 (35 > 10)

The side lengths 10, 20, and 15 form a triangle.

2) 8, 4, 12:
- 8 + 4 > 12 (12 > 12)
- 8 + 12 > 4 (20 > 4)
- 4 + 12 > 8 (16 > 8)

The side lengths 8, 4, and 12 form a triangle.

3) 8, 8, 20:
- 8 + 8 > 20 (16 > 20)
- 8 + 20 > 8 (28 > 8)
- 8 + 20 > 8 (28 > 8)

The side lengths 8, 8, and 20 do not form a triangle.

4) 20, 10, 30:
- 20 + 10 > 30 (30 > 30)
- 20 + 30 > 10 (50 > 10)
- 10 + 30 > 20 (40 > 20)

The side lengths 20, 10, and 30 form a triangle.