Apply the Triangle Inequsity 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 pont)

Question

The meniure of the third side could be or
Explain

Answer 1

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.

In this case, the first two sides measure 6 and 2.

So, applying the theorem, we have:
6 + 2 > x
8 > x

This means that the third side must be less than 8 units long.

However, the third side must also be greater than the difference of the lengths of the other two sides:
6 - 2 < x
4 < x

This means that the third side must be longer than 4 units.

Therefore, the possible whole number measures of the third side of the triangle are 5, 6, and 7 (since they are greater than 4 and less than 8). In ascending order, they are: 5, 6, 7.