Question

Based on the diagram, which expresses all possible lengths of segment AB?

Answer 1

B It should be the second answer choice

Answer 2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side (Triangle Inequality Theorem)

So

1) $AC+BC > AB$

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

2) $27+AB > 54$

$AB > 54-27\\ AB > 27$

3) $54+AB > 27$

$AB > 27-54\\ AB > -27$

therefore

the answer is

$27 < AB < 81$