Question

two sides of a triangle measure 4 and 6. which inequality shows all the possible lengths of the third side, x? a $\frac{2}{3}

Explanation:

Step1: Apply triangle - side rule

The length of the third side \(x\) of a triangle with side lengths \(a\) and \(b\) must satisfy the inequality \(|a - b|\lt x\lt a + b\). Here \(a = 4\) and \(b = 6\).

Step2: Calculate lower - bound

First, calculate \(|a - b|\): \(|4 - 6|=| - 2| = 2\).

Step3: Calculate upper - bound

Then, calculate \(a + b\): \(4+6 = 10\). So \(2\lt x\lt10\).

Answer:

C. \(2\lt x\lt10\)