Question

1. two sides of a triangle measure 3 meters and 8 meters. write an inequality to represent the perimeter of the triangle.

Explanation:

Step1: Recall Triangle Inequality

For a triangle with sides \(a\), \(b\), \(c\), the third side \(c\) must satisfy \(|a - b| < c < a + b\). Here, \(a = 3\), \(b = 8\), so the third side \(x\) (let's say) satisfies \(|8 - 3| < x < 8 + 3\), i.e., \(5 < x < 11\).

Step2: Define Perimeter

Perimeter \(P = 3 + 8 + x=11 + x\).

Step3: Find Perimeter Inequality

Since \(5 < x < 11\), add 11 to all parts: \(5 + 11 < 11 + x < 11 + 11\), so \(16 < P < 22\).

Answer:

The inequality representing the perimeter \(P\) of the triangle is \(16 < P < 22\)