Apply the Triangle Inequality Theorem and determine which option could be the third side of a triangle if the first two sides measure 4 and 6.(1 point)

Question

Responses

2
2

9
9

1
1

11

Answer 1

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

Let's check the options using the Triangle Inequality Theorem:

1. For the first two sides measuring 4 and 6:
- 4 + 6 = 10
- 10 is greater than the third side (2): True

2. For the first two sides measuring 4 and 6:
- 4 + 6 = 10
- 10 is not greater than the third side (9): False

3. For the first two sides measuring 4 and 6:
- 4 + 6 = 10
- 10 is greater than the third side (1): True

4. For the first two sides measuring 4 and 6:
- 4 + 6 = 10
- 10 is less than the third side (11): False

Therefore, the only option that could be the third side of a triangle with the first two sides measuring 4 and 6 is 1.