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: Recall Triangle Inequality Theorem

The triangle inequality theorem states that for a triangle with side lengths \(a\), \(b\), and \(x\) (the third side), the sum of any two sides must be greater than the third side, and the absolute difference of any two sides must be less than the third side. Mathematically, this is \(|a - b| < x < a + b\).

Step2: Identify \(a\) and \(b\)

Here, \(a = 300\) units and \(b = 200\) units. First, calculate the difference: \(|300 - 200| = 100\). Then, calculate the sum: \(300 + 200 = 500\).

Step3: Form the Compound Inequality

Using the triangle inequality theorem, the third side \(x\) must satisfy \(100 < x < 500\).

Answer:

\(100 < x < 500\)