I'm inclined to use Lingua::EN::Sentence to get the sentences, since it's a well-developed module for that purpose. Given this, perhaps the following will help:

use Modern::Perl;
use Lingua::EN::Sentence qw( get_sentences );

my ( $LRS, %seen ) = '';
my $sentences = 'Mr. Cat jumped over the dog. Smart Mr. Cat! He jumped
+ over the dog. Mr. Cat jumped over the dog.';
map { $seen{$_}++ and length $_ > length $LRS and $LRS = $_ }
  @{ get_sentences($sentences) };
say $LRS;
[download]

Output:

Mr. Cat jumped over the dog.
[download]

Update: Modified some sentences to challenge Lingua::EN::Sentence.