Question

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.

the measure of the third side could be ?, ?, or ?

Answer 1

In a triangle, the sum of the lengths of any two sides must always be greater than the length of the third side. This is known as the triangle inequality theorem.

Given that the first two sides have measures of 6 and 2, we can use the triangle inequality theorem to determine the possible whole number measures of the third side.

For the third side to be a valid length in the triangle, it must satisfy the following inequalities:
1. 6 + 2 > third side
2. 6 + third side > 2
3. 2 + third side > 6

Solving these inequalities, we get:
1. 8 > third side
2. 6 > third side - 2
3. third side > -4

Combining these inequalities, we get:
-4 < third side < 6

Therefore, the possible whole number measures of the third side are 0, 1, 3, 4, or 5 in ascending order.