dont think the height/width are in relation to eachother. i have seen a lot of short fat cases and long thin ones. jusr as much as you get short skinny and tall fat cases. the reason the SA doesnt fit you case is nothing to do with them not making the fans to fit all cases, its becuase they designed the fans to be the right size to make the product work efficiently (and keep the costs down). they give you dimensions so its up to you to make sure it fits.
Its difficult to go by measurement given in sale info, The Fractal R3 case is 207mm wide and the full tower version is 232mm wide, but then it depends how much room is left after fitting the m/b.
The Silver arrow says it is 160mm high, so how much room is actually left for a cooler when the m/b is in place