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 .

2 answers

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.

So, in this case, the third side must be greater than the difference between the first two sides and less than the sum of the first two sides.

The difference between 6 and 2 is 4, so the third side must be greater than 4.

The sum of 6 and 2 is 8, so the third side must be less than 8.

Therefore, the possible whole number measures of the third side are 5, 6, and 7.

Listing them in ascending order, the possible measures of the third side are: 5, 6, 7.
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