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

Answer 1

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

$27 < AB < 81$

Answer 2

The sum of the length of any two sides of the triangle is greater than the third side of the triangle. The third side is 81 > AB > 27.

What is the triangle?

Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.

Triangle basic theorem

The sum of the length of any two sides of the triangle is greater than the third side of the triangle.

Given

Length AC = 27 and Length BC = 54.

To find

The third side of the triangle.

How to find the third side of the triangle?

According to the theorem,

1.  AC + BC > AB, then

27 + 54 > AB

      AB < 81

2.  AC + AB > BC, then

27 + AB > 54

       AB > 54 - 27

       AB > 27

3.  AB + BC > AC, then

AB + 54 > 27

        AB > 27 - 54  

        AB > -27

Thus the third side is 81 > AB > 27.

More about the triangle link is given below.

https://brainly.com/question/25813512