my ($width,        $height       ) = ...;
my ($max_width,    $max_height   ) = (800, 600);
my ($width_factor, $height_factor) = ($max_width/$width, $max_height/$height);

if ($width_factor < 1 || $height_factor < 1) {
   my $factor = ($width_factor < $height_factor
      ? $width_factor
      : $height_factor
   );

   $width  = int($width  * $factor + 0.5);
   $height = int($height * $factor + 0.5);
}

##</code><code>##

use Image::Magick qw();

my $img = Image::Magick->new();

my $file_name = ...;
my $img->Read($file_name);

my ($width,        $height       ) = $img->Get(qw( width height ));
my ($max_width,    $max_height   ) = (800, 600);
my ($width_factor, $height_factor) = ($max_width/$width, $max_height/$height);

if ($width_factor < 1 || $height_factor < 1) {
   my $factor = ($width_factor < $height_factor
      ? $width_factor
      : $height_factor
   );

   my $new_width  = int($width  * $factor + 0.5);
   my $new_height = int($height * $factor + 0.5);

   $img->Resize(width => $new_width, height => $new_height);
   $img->Write($file_name);
}