The same way you do it for one file, only reading two instead. It would be nice to see what you've tried, so as to be able to help with whatever is your sticking point.

open FILEA, "< filea.txt" or die "Error opening filea.txt: $!";
open FILE1, "< file1.txt" or die "Error opening file1.txt: $!";
open FILEOUT, "> fileout.txt" or die "Error opening fileout.txt: $!";
while ( defined( my $lineA = <FILEA> ) && defined( my $line1 = <FILE1>
+ ) {
   chomp( $lineA, $line1 );
   print FILEOUT "$lineA $line1";
}
die "Eek!" if defined( $lineA ) || defined( $line1 );
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