Here is another way to solve the problem, using only basic functions and operators - very little other than what is in your original programs.

use strict;
use warnings;

my $longest = '';

for my $x (@ARGV) {
        if(length($x) > length($longest)) {
                $longest = $x;
        }
}

my $length = length($longest);
print "longest argument is '$longest' - length = $length\n";
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Here are a couple more issues for you to think about:

What should your program do if there are more than one arguments of the same, longest length. For example, what if the arguments were: abc def ghi?

What should your program do if there are no arguments?