Another way to do it: Text::Trim.

 
#!/usr/bin/perl -l

use strict;
use warnings;
use Text::Trim;

$|=1;

my @strings= <<"EOF";
This is a sentence in a paragraph. This a sentence in a paragraph.
 This is a sentence in a paragraph.

 This is a sentence in a paragraph. This a sentence in a paragraph.
 This is a sentence in a paragraph.
EOF

my $trimmed = trim(@strings);
print "\"$trimmed\"";
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