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.
(ONLY PICK ONE)
A. 2
B. 1
C. 9
D. 11
To apply the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the first two sides measure 4 and 6.
A. 2: 4 + 2 = 6, which is greater than 2.
B. 1: 4 + 1 = 5, which is greater than 1.
C. 9: 4 + 9 = 13, which is greater than 6.
D. 11: 4 + 11 = 15, which is greater than 6.
So, the third side can be 2 (option A), 1 (option B), 9 (option C), or 11 (option D).
Therefore, any of the options A, B, C, or D could be the third side of a triangle.