Question

a triangle has two sides of length 9 and 7. what is the largest possible whole - number length for the third side?

Explanation:

Step1: Apply triangle inequality theorem

The triangle inequality theorem states that for any triangle with side lengths \(a\), \(b\), and \(c\), \(a + b>c\), \(a + c>b\), and \(b + c>a\). Let the sides be \(a = 9\), \(b = 7\), and \(c\) be the third - side. Then \(c<9 + 7\) (from \(a + b>c\)).

Step2: Find the largest whole - number

Since \(c<16\) (because \(9+7 = 16\)), the largest whole - number less than \(16\) is \(15\).

Answer:

\(15\)