Question

enter the correct answer in the box.
a triangle has side lengths of 200 units and 300 units. write a compound inequality for the range of the possible lengths for the third side, x.

Explanation:

Step1: Apply the triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(|a - b|\lt c\lt a + b\). Here \(a = 200\) and \(b=300\).
First, calculate \(|a - b|\): \(|200 - 300|=| - 100| = 100\).
Second, calculate \(a + b\): \(200+300 = 500\).

Answer:

\(100\lt x\lt500\)