The lengths of the four sides of a quadrilateral (in centimeters) are consecutive odd integers. If the perimeter is 120 centimeters, find the value of the longest of the four side lengths.

Consecutive values represent a following value in a certain sequence. Since the sides are consecutive odd integers, we must add 2 to the previous side to get the next one.

Solving:

[tex]\section*{}Side Lengths(s) :\[s, \quad s+2, \quad s+4, \quad s+6\]Set up the equation to equal the perimeter of 120 centimeters:\[s + (s + 2) + (s + 4) + (s + 6) = 120\]Combine like terms:\[4s + 12 = 120\]Subtract 12 from both sides to isolate the term with \(s\):\[4s = 108\][/tex]

[tex]\\\section*{}Divide both sides by 4 to solve for \(s\):\[\boxed{s = 27}\]Now, the side lengths are:\[s = 27\]\[s + 2 = 29\]\[s + 4 = 31\]\[\boxed{s + 6 = 33}\][/tex]

As you can see, the largest side is 33 centimers.