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.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Given that two sides of the triangle have lengths 5.2 and 8.1, let's determine the range of values for the third side.
The sum of the lengths of the two known sides is 5.2 + 8.1 = 13.3.
Let's denote the length of the third side as x.
The inequality for the triangle is:
5.2 + 8.1 > x
13.3 > x
Therefore, the range of values for the third side of the triangle is x < 13.3.
In conclusion, the third side of the triangle must be less than 13.3.