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

11
11

9
9

1

Answer 1

To determine which option could be the third side of a triangle, we can use the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

In this case, the first two sides measure 4 and 6. Let's analyze each option:

1) Option 2, 2: The sum of the first two sides is 4 + 6 = 10. The third side would need to be smaller than 10 to satisfy the Triangle Inequality Theorem. Therefore, option 2, 2 could be the third side of a triangle.

2) Option 11, 11: The sum of the first two sides is 4 + 6 = 10. The third side would need to be greater than 10 to satisfy the Triangle Inequality Theorem. Therefore, option 11, 11 could not be the third side of a triangle.

3) Option 9, 9: The sum of the first two sides is 4 + 6 = 10. The third side would need to be greater than 10 to satisfy the Triangle Inequality Theorem. Therefore, option 9, 9 could not be the third side of a triangle.

4) Option 1: A single number cannot be considered as a side length for a triangle, so option 1 could not be the third side of a triangle.

Based on the Triangle Inequality Theorem, the only valid option for the third side of a triangle is 2.