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 triangle inequality theorem (difference)

Let the sides be \(a = 6\), \(b=15\), \(c\) be the third side.
By \(|a - b|\lt c\), we have \(|6 - 15|\lt c\), so \(9\lt c\).

Step2: Apply triangle inequality theorem (sum)

By \(a + b\gt c\), we have \(6+15\gt c\), so \(c\lt21\).

Answer:

The possible lengths of the third side \(c\) satisfy \(9\lt c\lt21\) (where \(c\) is measured in yards).