Question

two sides of a triangle are 10 and 17. find the range of possible side lengths for the third side. type your answer as an inequality with appropriate symbols, using x as your variable. type your answer as an inequality like we did in the notes with appropriate symbols, using x as your variable.

Explanation:

Step1: Apply triangle - inequality theorem (sum of two sides)

The sum of any two sides of a triangle must be greater than the third side. So \(x<10 + 17\), which simplifies to \(x<27\).

Step2: Apply triangle - inequality theorem (difference of two sides)

The difference between any two sides of a triangle must be less than the third side. So \(|17 - 10|

Answer:

\(7