Question

27

Answer 1

Sum of any two sides must be greater than third one

Sum of rest two

• 27+54
• 81

AB must be greater than 85

Option C

Answer 2

Answer: 27<AB<81

Step-by-step explanation:

We can generalize the triangle inequality theorem to say that the sum of the lengths of the two shorter sides must be greater than the length of the longest side.

Case 1: AB is the longest side

$27+54 > AB\\AB < 81$

Case 2: BC is the longest side

$27+AB > 54\\AB > 27$

So, $\boxed{27 < AB < 81}$