Question

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

Answer 1

Not quite true.
If the third side is x, then we must have
8.2 - 3.7 < x < 8.2 + 3.7
4.5 < x < 11.9

Answer 2

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.

Let's apply this theorem to the given lengths of 3.7 and 8.2:

1. The sum of the lengths of the two sides must be greater than the length of the third side:
3.7 + 8.2 > third side length

2. Solve the inequality for the third side length:
11.9 > third side length

Therefore, a possible measure of the third side could be any value less than 11.9.

Answer 3

Apologies for the mistake. You are correct.

Applying the Triangle Inequality Theorem, the possible measure of the third side, denoted as x, would be:

8.2 - 3.7 < x < 8.2 + 3.7
4.5 < x < 11.9

Thus, the possible measure of the third side is any value between 4.5 and 11.9.