Question

Apply the Triangle Inequality Theorem to determine which three side lengths form a triangle.(1 point)

Responses

20, 10, 30
20, 10, 30

8, 4, 12
8, 4, 12

10, 20, 15
10, 20, 15

8, 8, 20

Answer 1

[AI-generated answer — Bot GPT 3.5]

In order to use the Triangle Inequality Theorem, we need to check if the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

1. For the first set of side lengths (20, 10, 30):
- 20 + 10 = 30 which is equal to 30, so this does not form a triangle.

2. For the second set of side lengths (8, 4, 12):
- 8 + 4 = 12 which is equal to 12, so this does not form a triangle.

3. For the third set of side lengths (10, 20, 15):
- 10 + 15 = 25 which is greater than 20, so this forms a triangle.

4. For the fourth set of side lengths (8, 8, 20):
- 8 + 8 = 16 which is less than 20, so this does not form a triangle.

Therefore, the side lengths 10, 20, 15 form a triangle according to the Triangle Inequality Theorem.