In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Let's denote the lengths of the three sides of the triangle as a, b, and c.
In this case, we are given that two sides have lengths 5.2 and 8.1. Let's assume the third side has length c.
According to the triangle inequality theorem, we have the following inequalities:
a + b > c
a + c > b
b + c > a
Substituting the given values, we have:
5.2 + 8.1 > c
c < 13.3
5.2 + c > 8.1
c > 2.9
8.1 + c > 5.2
c > -2.9
Combining these inequalities, we find that the range of values for the third side of the triangle is 2.9 < c < 13.3.
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
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