It's not quite as trivial as it might seem at first (most of us who have tried probably got it wrong the first time :)

Just as an example, take a width of 1000 and a height of 100. Your algorithm would compute 6000x600 (W x H), although the expected result would be 800x80 (i.e. max width doesn't exceed 800 and aspect ratio stays at 10:1)