apply the triangle inequality theorem and determine which option could be the 3rd side of a triangle if the first 2 sides measure 4 and 6.

Question

1. 9
2. 1
3. 11
4. 2

Answer 1

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.

Given that the first 2 sides measure 4 and 6:

1. 9: 4 + 6 > 9, so it is a valid third side.
2. 1: 4 + 6 > 1 is not true, so it cannot be a valid third side.
3. 11: 4 + 6 > 11 is not true, so it cannot be a valid third side.
4. 2: 4 + 6 > 2 is not true, so it cannot be a valid third side.

Therefore, the only option that could be the 3rd side of a triangle is 9.