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 ___.
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 the first two sides are 6 and 2, the third side must satisfy the following conditions:
1. 6 + 2 > x
2. 6 + x > 2
3. 2 + x > 6
Solving these inequalities, we find that the third side must be:
1. 6 + 2 > x -> 8 > x
2. 6 + x > 2 -> x > -4
3. 2 + x > 6 -> x > 4
Combining all three conditions, the possible whole number measures of the third side are 5, 6, 7.
So, the third side could be 5, 6, or 7.