To answer this, you will want to find the perimeter in terms of x first. To do this, you just add all the lengths of the sides together: x + (x + 1) + (x + 8) + (x + 5) + (x + 4) + (x + 6) = 6x + 24 = 150.
Solve for x, and you get that x = 21. The longest side is obviously x + 8, so you do 21 + 8 = 29 cm.