Question

jamie knows the lengths of 2 sides of a triangle are 8 and 12. use the triangle inequality theorem to determine the possible values for the length of the third side of jamies triangle. 0 < s < 4 0 < s < 20 4 ≤ s ≤ 20 4 < s < 20

Explanation:

Step1: Apply the triangle inequality theorem (difference of two sides)

Let the two given sides be \(a = 8\) and \(b=12\). The difference of two sides of a triangle \(|a - b|\lt s\). So \(|12 - 8|\lt s\), which simplifies to \(4\lt s\).

Step2: Apply the triangle inequality theorem (sum of two sides)

The sum of two sides of a triangle \(a + b>s\). So \(8 + 12>s\), which simplifies to \(20>s\).

Combining the two inequalities \(4\lt s\) and \(s\lt20\) gives \(4\lt s\lt20\).

Answer:

\(4\lt s\lt20\) (the fourth option)