Question

based on the diagram, which expresses all possible lengths of segment ab? ab = 25 27 < ab < 81 ab = 85 ab < 27 or ab > 81

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 of a triangle must be less than the length of the third side. Let the sides of the triangle be \(a = 27\), \(b=54\), and \(c = AB\).

Step2: Apply the first part of the theorem

\(a + b>c\) and \(b + c>a\) and \(c + a>b\). Also, \(|a - b|

Step3: Calculate the range

\(54-27=27\) and \(54 + 27=81\). So, \(27

Answer:

B. \(27