Question

two of a triangles side lengths are 20 cm and 28 cm. what is the largest possible whole number length of the third side?

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Let the sides of the triangle be \(a = 20\) cm, \(b = 28\) cm, and \(c\) be the third - side. Then \(a + b>c\), \(a + c>b\), and \(b + c>a\). To find the largest possible value of \(c\), we use the inequality \(a + b>c\).

Step2: Calculate the upper - bound

We know that \(c < a + b\). Substituting \(a = 20\) cm and \(b = 28\) cm, we get \(c<20 + 28=48\) cm.

Step3: Determine the largest whole - number value

Since \(c\) is a whole number and \(c<48\), the largest whole - number value of \(c\) is 47 cm.

Answer:

47