Question

1. a triangle has one side of 5 cm and another of 17 cm. what are the possible lengths of the third side? the outlined content above was added from outside of formative. 12 < x < 17 12 < x < 22 5 ≤ x ≤ 17 5 < x < 17 12 ≤ x ≤ 22 app.formative.com

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 \(a = 5\) cm, \(b = 17\) cm, and \(c\) be the third - side. Then \(a + c>b\), \(a + b>c\), and \(b + c>a\). Also, \(|a - b|

Step2: Calculate the lower - bound

The difference between the two given sides gives the lower - bound of the third side. \(|17 - 5|=12\). So \(c>12\).

Step3: Calculate the upper - bound

The sum of the two given sides gives the upper - bound of the third side. \(17 + 5 = 22\). So \(c<22\).

Answer:

B. \(12 < x < 22\)