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)
In a triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's call the unknown length of the third side x.
So we have two inequalities:
x + 5.2 > 8.1 (using the given lengths)
x > 2.9
and
x + 8.1 > 5.2
x > -2.9 (subtracting 8.1 from both sides)
The range of values for the third side of the triangle is x > 2.9, since a negative length for a side doesn't make geometric sense.