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
20, 10, 30

Answer 1

To determine which three side lengths can form a triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Let's evaluate each set of side lengths one by one.

1. **10, 20, 15**:
- 10 + 20 = 30 > 15 (valid)
- 10 + 15 = 25 > 20 (valid)
- 20 + 15 = 35 > 10 (valid)
- All conditions are satisfied, so these can form a triangle.

2. **8, 4, 12**:
- 8 + 4 = 12 (not greater than 12)
- Since this fails, these cannot form a triangle.

3. **8, 8, 20**:
- 8 + 8 = 16 < 20 (not greater than 20)
- Since this fails, these cannot form a triangle.

4. **20, 10, 30**:
- 20 + 10 = 30 (not greater than 30)
- Since this fails, these cannot form a triangle.

From the evaluation above, the only set of side lengths that can form a triangle is:

**10, 20, 15**.