Question

1. if the lengths of two sides of a triangle are 5 and 7, the length of the third side may not be: (a) 12 (b) 7 (c) 3 (d) 5

Explanation:

Step1: Recall triangle - side rule

The length of the third side \(x\) of a triangle with two side - lengths \(a\) and \(b\) satisfies the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 5\) and \(b = 7\).

Step2: Calculate the range

First, calculate \(|5 - 7|=2\) and \(5 + 7 = 12\). So the range of the third - side length \(x\) is \(2\lt x\lt12\).

Answer:

A. 12