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 if a third side could be the 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.
In this case, the first two sides measure 4 and 6. We can test each option to see which ones satisfy the Triangle Inequality Theorem:
A. 2
4 + 2 = 6, which is equal to the length of the second side. Therefore, this option does not satisfy the Triangle Inequality Theorem.
B. 1
4 + 1 = 5, which is less than the length of the second side. Therefore, this option does not satisfy the Triangle Inequality Theorem.
C. 9
4 + 9 = 13, which is greater than the length of the second side. Therefore, this option satisfies the Triangle Inequality Theorem.
D. 11
4 + 11 = 15, which is greater than the length of the second side. Therefore, this option satisfies the Triangle Inequality Theorem.
Based on the Triangle Inequality Theorem, the options that could be the third side of a triangle are:
C. 9
D. 11