the measure of two sides of a triangle and 5.2 and 8.1. Determine the range of values for the third values for the third side of the triangle
__ < n < __
To find the range of values for the third side of the triangle, we can use the triangle inequality theorem. According to the 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 call the third side of the triangle "n".
Using the triangle inequality theorem, we can write the following inequalities:
5.2 + 8.1 > n (The sum of the two given sides is greater than the third side)
5.2 + n > 8.1 (The sum of one given side and the third side is greater than the other given side)
8.1 + n > 5.2 (The sum of one given side and the third side is greater than the other given side)
Simplifying these inequalities, we have:
13.3 > n
n > 3.1
n > -3.1
Therefore, the range of values for the third side of the triangle is 3.1 < n < 13.3.