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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
To apply the Triangle Inequality Theorem, we must have 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, we can determine the possible whole number measures of the third side by considering the inequalities:
1. 2 + 6 > x
2. 6 + x > 2
3. 2 + x > 6
Solving these inequalities:
1. 2 + 6 > x
8 > x
2. 6 + x > 2
x > -4
3. 2 + x > 6
x > 4
Therefore, the possible whole number measures of the third side can be 5, 6, or 7.
Listing them in ascending order: 5, 6, 7.