The measures of two sides of a triangle are 5.2 and 8.1. Determine the range of values for the third side of the triangle.(1 point)
____ < n < ____
To determine the range of values for the third side of a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.
In this case, let's consider the two given sides: 5.2 and 8.1.
The third side should satisfy the following inequalities:
5.2 + x > 8.1 [where x represents the length of the third side]
8.1 + x > 5.2
5.2 + 8.1 > x
From the first equation, we have:
x > 8.1 - 5.2
x > 2.9
From the second equation, we have:
x > 5.2 - 8.1
x > -2.9
From the third equation, we have:
13.3 > x
Therefore, the range of values for the third side is:
2.9 < x < 13.3