#!/usr/bin/perl

use warnings;
use strict;

my $height = "1000";
my $width = "1234";

my $maxh = "600";
my $maxw = "800";

if ($height > $maxh || $width > $maxw)
{
    my $hratio = $height / $maxh;
    my $wratio = $width / $maxw;

    my $newh = $height / $hratio;
    my $neww = $width / $hratio;

   print "Height is now $newh, Width is now $neww";  
}

RESPONSE FROM ALMUT: 
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)