Question

Find the range for the measure of the third side of a triangle given the measures of two sides are 18 ft and 23 ft.

___ft < n < ___ft

Answer 1

Answer: 5 ft < n < infinity

Explanation:

To find the range for the measure of the third side of a 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.

Let's call the measure of the third side "n".

According to the triangle inequality theorem, for a triangle with side lengths of 18 ft, 23 ft, and "n" ft, we have:

18 + n > 23 and 23 + n > 18

Solving these inequalities, we get:

18 + n > 23

n > 23 - 18

n > 5

and

23 + n > 18

n > 18 - 23

n > -5

Therefore, the range for the measure of the third side of the triangle is:

5 ft < n < infinity