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
2
11
9
1
The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to the given options:
1) 2: 4 + 2 = 6, which is equal to the third side and violates the triangle inequality theorem.
2) 11: 4 + 11 = 15, which is greater than the third side.
3) 9: 4 + 9 = 13, which is greater than the third side.
4) 1: 4 + 1 = 5, which is greater than the third side.
Therefore, the only option that could be the third side of a triangle with the first two sides measuring 4 and 6 is 9.