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) Responses 11 11 2 2 9 9 1
To determine if a given option could be the third side of a triangle, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Given the first two sides are 4 and 6, let's check if each of the options satisfies the theorem:
1. 11: 4 + 6 > 11, 6 + 11 > 4, 4 + 11 > 6. True
2. 2: 4 + 6 > 2, 6 + 2 < 4, 4 + 2 > 6. False
3. 9: 4 + 6 > 9, 6 + 9 > 4, 4 + 9 > 6. True
4. 1: 4 + 6 > 1, 6 + 1 < 4, 4 + 1 < 6. False
Therefore, the options that could be the third side of a triangle are 11 and 9.