Question

nguyen wants to draw a triangle with side lengths of 8 millimeters and 6 millimeters. which of the following cannot be the length of the third side? 8 9 12 2

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), the following must hold: \(|a - b|\lt c\lt a + b\). Here \(a = 8\) and \(b=6\). First, calculate \(|8 - 6|=2\) and \(8 + 6=14\). So the length of the third side \(c\) must satisfy \(2\lt c\lt14\).

Step2: Check each option

• For \(c = 8\): Since \(2\lt8\lt14\), 8 can be the length of the third side.
• For \(c = 9\): Since \(2\lt9\lt14\), 9 can be the length of the third side.
• For \(c = 12\): Since \(2\lt12\lt14\), 12 can be the length of the third side.
• For \(c = 2\): Since \(2 = 2\) (does not satisfy \(2\lt c\)), 2 cannot be the length of the third side.

Answer:

2