(PICK ONE)
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.
A. 2
B. 1
C. 9
D. 11
To determine which option could be the third side of a triangle, we can use 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.
Let's check each option:
A. 2: 4 + 2 = 6, which is equal to the length of the second side. This is not greater, so option A is not a valid third side for a triangle.
B. 1: 4 + 1 = 5, which is less than the length of the second side. This is not greater, so option B is not a valid third side for a triangle.
C. 9: 4 + 9 = 13, which is greater than the length of the second side. This option satisfies the Triangle Inequality Theorem and could be the third side of a triangle.
D. 11: 4 + 11 = 15, which is greater than the length of the second side. This option also satisfies the Triangle Inequality Theorem and could be the third side of a triangle.
Therefore, the options that could be the third side of a triangle are C. 9 and D. 11.