Question

1. a triangle has one side 6 yards and another 15 yards. what are the possible lengths of the third side?

Explanation:

Step1: Apply the triangle inequality theorem

Let the sides of the triangle be \(a = 6\), \(b=15\), and \(c\) be the third - side.
The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. So \(a + b>c\), \(a + c>b\), and \(b + c>a\).
From \(a + b>c\), we have \(6 + 15>c\), i.e., \(c<21\).
From \(b - ab\) rewritten as \(c>b - a\)), we have \(15-6 < c\), i.e., \(c > 9\).

Answer:

The possible lengths of the third side \(c\) satisfy \(9\) yards\(