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. 11
C. 9
D. 1
To determine if a number could be the third side of a triangle, we need to check if it satisfies the Triangle Inequality Theorem. According to the theorem, 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
Since 6 is equal to the third side (2), this option satisfies the Triangle Inequality Theorem.
B. 11
4 + 11 = 15
Since 15 is greater than 6, this option satisfies the Triangle Inequality Theorem.
C. 9
4 + 9 = 13
Since 13 is greater than 6, this option satisfies the Triangle Inequality Theorem.
D. 1
4 + 1 = 5
Since 5 is less than 6, this option does not satisfy the Triangle Inequality Theorem.
So, the third side of a triangle could be 2, 11, or 9. The correct options are A, B, and C.