Apply the Triangle Inequality Theorem to determine the possible whole number measures of the third side of a triangle if the first two sides measure 6 and 2. List them in ascending order.(2 points)
The measure of the third side could be
____,
____, or
____.
The Triangle Inequality Theorem states that 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 two sides measure 6 and 2 respectively, we can calculate the range of possible measures for the third side by considering the inequalities:
- 6 + 2 > x
- 6 + x > 2
- 2 + x > 6
Solving the inequalities:
- 8 > x
- 6 > x
- 8 > x
Therefore, the possible whole number measures of the third side in ascending order are 3, 5, 7.