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
4.5
4.2
3.5
5.5
What is the correct answer
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.