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.(

Answer 1

In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side for the triangle to exist.

Let's call the third side of the triangle x.

Using the Triangle Inequality Theorem, we can write the following inequality:

5.2 + 8.1 > x

By summing the lengths of the given sides, we get:

13.3 > x

Therefore, the third side must be less than 13.3 units.

Additionally, since a side length cannot be negative, the third side must also be greater than 0 units.

Therefore, the range of values for the third side of the triangle is 0 < x < 13.3.

Answer 2

The 0 is wrong

Answer 3

My apologies for the incorrect response. You are right, the length of any side of a triangle cannot be zero.

To determine the range of values for the third side of the triangle, we need to apply the Triangle Inequality Theorem again:

The sum of the lengths of the two given sides must be greater than the length of the third side.

For side lengths 5.2 and 8.1, we have:

5.2 + 8.1 > x

13.3 > x

So the third side must be shorter than 13.3 units, maintaining the strict inequality.

However, it is also important to note that the length of the third side must be longer than the difference between the lengths of the two given sides:

8.1 - 5.2 < x

2.9 < x

Therefore, the range of values for the third side of the triangle is 2.9 < x < 13.3.