my $string=`wc -l $filename`;
my ($file,$length)=split " ",$filename;
chomp($length);
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That looks a bit off to me. First of all, $string contains the information, but you are splitting $filename. Secondly, every wc implementation that I've ever seen outputs the linecount before the filename, but you have them reversed....

If I were going to rewrite this snippet and was forced to use wc, I might do something like:

#!/usr/bin/perl -wT
use strict;
%ENV = (PATH => '/bin:/usr/bin');  # give us a happy enviornment

my $filename = '/etc/services';    # filename to be checked

my $length = do {
  my $string = `wc -l $filename`;  # get output of wc 
  die "wc error $?" if $?;         # die if wc chokes for some reason
  no warnings 'numeric';           # turn off a pesky warning ;-)
  $string + 0;                     # numerify it with +0
};

print "length = $length\n";        # "length = 331" on my machine
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Update:
*sigh* /g still gives me trouble some times.... The numerify line above could also have been:

 ($string =~ /\d+/g)[0];
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which would eliminate the need to turn off the warning. Therefore, the above can all be squeezed down into:

my $length = (`wc -l $filename` =~ /\d+/g)[0];  # get output of wc
die "wc error $?" if $?;        # die if wc chokes for some reason
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-Blake