$lines = 56;
$filename = 'chapterx.html';
$nameformat = 'chapterx_page_%d.html';

open(INFILE, "<$filename") or die $!;
while(<INFILE>) {
    if ($. % $lines == 1) {
        open(OUTFILE, '>'.sprintf($nameformat, $. / $lines + 1)) or die $!;
    }                                                           
    print OUTFILE $_;                                           
}