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.

Question

The measure of the third side could be 5,6,7

Answer 1

In order 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.

For the given triangle with sides measuring 6 and 2, the possible values for the third side can be found by evaluating the following inequalities:

1. 6 + 2 > x
8 > x

2. 6 + x > 2
6 + 2 > x
8 > x

3. 2 + x > 6
8 > x

Therefore, the possible whole number measures of the third side are 5, 6, and 7. Sorting them in ascending order gives: 5, 6, 7.