Question

1. multiple choice: which is a possible length for the third side of a triangle with side lengths 14 and 19? (a) 33 (b) 27 (c) 4 (d) 5 what are the minimum and maximum values possible?

Explanation:

Step1: Recall triangle - inequality theorem

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 14\) and \(b = 19\).

Step2: Calculate the lower - bound

\(|19 - 14|=5\), so \(x>5\).

Step3: Calculate the upper - bound

\(19 + 14=33\), so \(x<33\).

Answer:

B. 27