If you want to do bioinformatics with Perl, may I recommend getting familiar with Bioperl (http://bioperl.org/). It provides modules for FASTA format parsing (and many other formats. Your homework is then very easy :)

use Bio::SeqIO;
$in  = Bio::SeqIO->new(-file => "inputfilename",-format => 'Fasta');
while ( my $seq = $in->next_seq() ) {
   $seqstr   = $seq->seq(); # actual sequence as a string
   print $seqobj->display_id(); # human readable id of the sequence
   print length($seqstr); # length of sequence
}
[download]

Code is untested and largely lifted from the Bioperl tutorial.