Investigating progressive numbers (Euler, 141)

-- ### Project Euler, problem 141 ### --
import Data.List (sort)

intToDouble :: Int -> Double
intToDouble n = fromIntegral n :: Double

ratio :: (Int, Int, Int) -> Double
ratio (a, b, c) | 0 `notElem` [a, b, c] = (\(x:y:z:_) -> if x/y == y/z then x/y else 0.0) . sort $ map intToDouble [a, b, c]
                | otherwise = 0.0

progressive :: Int -> Bool
progressive n = any (== True) $ map (\d -> ratio (d, n `div` d, n `mod` d) /= 0.0) [2..n `div` 2]

perfectSquare :: Int -> Bool
perfectSquare n = (squareRoot n) == (fromIntegral . truncate $ squareRoot n)
  where
    squareRoot = sqrt . fromIntegral

solveit n = filter (apply3f perfectSquare progressive (&&)) [1..n]
  where
    apply3f f1 f2 f3 x = f3 (f1 x) (f2 x)

main = do
  putStrLn . show . sum $ solveit 100000