Question

the lengths of 2 sides of a triangle are 6 and 13. which of the following could be the perimeter of the triangle? check with your teacher to see if you got the correct answer on this one. 19 26 38 34

Explanation:

Step1: Recall triangle - inequality theorem

Let the sides of the triangle be \(a = 6\), \(b = 13\), and \(c\) be the third - side. According to the triangle - inequality theorem, \(|a - b|\lt c\lt a + b\). So, \(|6 - 13|\lt c\lt6 + 13\), which simplifies to \(7\lt c\lt19\).

Step2: Calculate the perimeter range

The perimeter \(P=a + b + c=6 + 13 + c=19 + c\). Since \(7\lt c\lt19\), then \(19+7\lt P\lt19 + 19\), or \(26\lt P\lt38\).

Answer:

34