Question

The measure of two sides of a triangle are 7 and 11. Determine the range of values for the third side of the triangle.

< n <

Answer 1

[AI-generated answer — Bot GPT 3.5]

4 < n < 18

Answer 2

explain how its done

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine the range of values for the third side of the 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 third side.

In this case, the two given sides are 7 and 11. So we can set up two inequalities to satisfy the triangle inequality theorem:

1. The sum of the two given sides must be greater than the third side:
7 + 11 > n
18 > n

2. The difference of the two given sides must be less than the third side:
|7 - 11| < n
4 < n

Therefore, the third side (n) must be greater than 4 and less than 18 in order to form a valid triangle. The range of values for the third side is 4 < n < 18.