(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
D. 11
To determine which option could be the third side of a triangle, we can 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.
Therefore, for a triangle with side lengths of 4 and 6, the third side must satisfy the inequality:
4 + 6 > third side length
Simplifying the inequality, we get:
10 > third side length
Option A: 2
4 + 2 = 6 < 10, so this option does not satisfy the inequality.
Option B: 1
4 + 1 = 5 < 10, so this option does not satisfy the inequality.
Option D: 11
4 + 11 = 15 > 10, so this option satisfies the inequality.
Therefore, option D, with a length of 11, could be the third side of a triangle with side lengths of 4 and 6.