Question

a triangles side lengths are whole numbers. if the measure of two of its sides are 1 cm and 13 cm, what is the measure of the third side? (1 point)

12.5 cm
12 cm
13 cm
1 cm

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, and the difference between the lengths of any two sides must be less than the length of the third side. Let the sides of the triangle be \(a = 1\) cm, \(b = 13\) cm, and \(c\) be the third - side. Then \(|a - b|\lt c\lt a + b\).

Step2: Calculate the range of the third - side

First, calculate \(|1 - 13|=12\) and \(1+13 = 14\). So, \(12\lt c\lt14\).

Step3: Select the appropriate value

Since the side lengths are whole numbers, the only whole - number value for \(c\) in the range \(12\lt c\lt14\) is \(13\) cm.

Answer:

C. 13 cm