Apply the triangle inequality THEOREN and determine which option could be the third side of a triangle if the two sides of a triangle measure four and 6
Two
11
Nine
One
According to 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 two sides of 4 and 6, let's check which option could be the third side:
1. 4 + 6 > 2
- 10 > 2 (True)
2. 4 + 6 > 11
- 10 > 11 (False)
3. 4 + 6 > 9
- 10 > 9 (True)
4. 4 + 6 > 1
- 10 > 1 (True)
Therefore, the option that could be the third side of a triangle with sides of 4 and 6 is Nine.