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?
Pick three numbers
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.
Given that the first two sides measure 6 and 2, the possible whole number measures of the third side can be determined by checking whether the sum of each pair of sides is greater than the third side.
For example:
- If the third side is 1, then 6 + 2 is not greater than 1. Thus, 1 is not a possible measure of the third side.
- If the third side is 3, then 6 + 2 is greater than 3. So, 3 is a possible measure of the third side.
- If the third side is 4, then 6 + 2 is greater than 4. So, 4 is a possible measure of the third side.
- If the third side is 5, then 6 + 2 is greater than 5. So, 5 is a possible measure of the third side.
- If the third side is 6, then 6 + 2 is equal to 6. The third side cannot be equal to the sum of the other two sides in a triangle, so 6 is not a possible measure of the third side.
Therefore, the possible whole number measures of the third side, in ascending order, are 3, 4, and 5.