Question

an acute triangle has two sides measuring 8 cm and 10 cm. what is the best representation of the possible range of values for the third side, s? 2 < s < 18 6 < s < 12.8 s < 2 or s > 18 s < 6 or s > 12.8

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 two given side - lengths be \(a = 8\) cm and \(b = 10\) cm.

Step2: Calculate the lower - bound

The lower - bound of the third side \(s\) is given by \(|a - b|\). So, \(|8 - 10|=2\) cm.

Step3: Calculate the upper - bound

The upper - bound of the third side \(s\) is given by \(a + b\). So, \(8+10 = 18\) cm.

Answer:

\(2\lt s\lt18\)