Question

1. a triangle has one side 21 meters and another 16 meters. describe the possible lengths of the third side.

Explanation:

Step1: Apply triangle inequality theorem

Let the sides of the triangle be \(a = 21\), \(b=16\), and \(c\) (the third - side). The triangle inequality theorem states that for any triangle, \(a + b>c\), \(a + c>b\), and \(b + c>a\).
From \(a + b>c\), we have \(21 + 16>c\), so \(c<37\).
From \(a + c>b\) (which is always true since \(a>b\) and \(c>0\)) and \(b + c>a\), we get \(c>21 - 16\).

Step2: Calculate the lower - bound

\(21-16 = 5\).

Answer:

The length of the third side \(c\) must satisfy \(5\lt c\lt37\) meters.