Apply the Triangle Inequality Theorem and determine which option could be the third side of the triangle if the two sides measure 4 and 6?
A) 1
B) 9
C) 11
D) 2
pick one
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.
- Option A) 4 + 1 = 5 and 5 < 6. This does not satisfy the theorem, so option A) cannot be the third side of the triangle.
- Option B) 4 + 9 = 13 and 13 > 6. This satisfies the theorem, so option B) could be the third side of the triangle.
- Option C) 4 + 11 = 15 and 15 > 6. This satisfies the theorem, so option C) could be the third side of the triangle.
- Option D) 4 + 2 = 6 and 6 = 6. This does not satisfy the theorem as the lengths of the two sides should be greater than the length of the third side. Therefore, option D) cannot be the third side of the triangle.
Based on the Triangle Inequality Theorem, options B) and C) could possibly be the third side of the triangle.