Two sides of a triangle measure 3.7 and 8.2. Apply the Triangle Inequality Theorem to find a possible measure of the third side.(1 point) Responses 4.2 4.2 3.5 3.5 4.5 4.5 5.5
The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Therefore, to find a possible measure of the third side, we need to determine the range of possible values based on this theorem.
Let's consider the given measurements: 3.7 and 8.2.
For the third side to be valid, the sum of the 3.7 and 8.2 must be greater than the length of the third side: 3.7 + 8.2 > third side
11.9 > third side
This means that the possible measures of the third side must be less than 11.9.
Looking at the provided options, the only possible measure of the third side is 4.5. Therefore, the answer is 4.5.