@in = (                                 
        ['the cat', 'sat', 'on', 'the', 'mat'],               
        ['the cat sat', 'wherever if felt like'],                          
        ['the cat'],                           
                              
);  

my @out =  map{$_->[0]}  sort{$a->[1] cmp $b->[1]}  map{[$_, concat($_)]} @in;

sub concat {
    my $ary = shift;
    $ary = join '', @$ary;
    $ary =~ s/\s//g;
  return $ary;
}

use Data::Dumper;
$Data::Dumper::Indent = 0;
print map {s/\[/\n        \[/g; $_} Dumper \@out;

__DATA__
$VAR1 = 
        [
        ['the cat'],
        ['the cat','sat','on','the','mat'],
        ['the cat sat','wherever if felt like']];