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.(1 point)
What are the two answers

Answer 1

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.

For the given triangle, let's call the lengths of the sides 7, 11, and x. According to the triangle inequality theorem, we have the following inequalities:

7 + 11 > x (sum of the two given sides must be greater than x)
7 + x > 11 (sum of the given side and the third side must be greater than 11)
11 + x > 7 (sum of the given side and the third side must be greater than 7)

Simplifying these inequalities, we have:

18 > x
x > 4
x > -4

Therefore, the range of values for the third side of the triangle is x such that -4 < x < 18.