The aptly named screenwidth and screenheight methods of the MainWindow will give you that info. They are documented in Tk::Wm. While the documentation for Tk is good, it takes some searching to find relevant info. I own a copy of "Mastering Perl/Tk", and it's a good reference to have on hand.
Here's a quick example:
my $mw = MainWindow->new;
$mw->Label( -text => $mw->screenheight . " x ". $mw->screenwidth )->p
On this computer, it gives me "1280 x 1024"