Question

in a certain triangle the length of two sides are 1.9 m and 0.7 m. what is the length of the third side if you know that it should be a whole number? answer: the length of the third side is m

Explanation:

Step1: Recall triangle - inequality theorem

Let the sides of the triangle be \(a = 1.9\) m, \(b = 0.7\) m and \(c\) be the third - side. According to the triangle - inequality theorem, \(|a - b|\lt c\lt a + b\).

Step2: Calculate the lower and upper bounds

First, calculate \(|a - b|\): \(|1.9−0.7|=1.2\) m. Then calculate \(a + b\): \(1.9 + 0.7=2.6\) m. So, \(1.2\lt c\lt2.6\).

Step3: Find the whole - number value

Since \(c\) is a whole number and \(1.2\lt c\lt2.6\), the only whole - number in this range is \(2\) m.

Answer:

2