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

Question

4.5

4.2

3.5

5.5

What is the correct answer

Answer 1

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.

In this case, let's consider the two given sides: 3.7 and 8.2.

Using the triangle inequality theorem, we can check if the sum of these two sides is greater than the length of the third side:

3.7 + 8.2 = 11.9

Now, let's check the options given:

- 4.5: 3.7 + 4.5 = 8.2 (less than 11.9)
- 4.2: 3.7 + 4.2 = 7.9 (less than 11.9)
- 3.5: 3.7 + 3.5 = 7.2 (less than 11.9)
- 5.5: 3.7 + 5.5 = 9.2 (less than 11.9)

Since none of the options satisfy the triangle inequality theorem, none of them are a possible measure for the third side.