I also came up with five 3.5 X 36 inch strips (same as Bearisgray). This is with straight joining seams, not diagonal.
5 X 36 = 180. Less 2" for joining seams 178. You will also need an additional length of fabric for the corners as you add the borders, but the 178" will accommodate this (This is a border, correct?)
This assumes very accurate cutting, as there will only be a 1/2" strip left. Also assumes that your small piece is cut square to start out with. If it's not square, or you sometimes have problems with your cutting, then I would go for 3" strips.