I'd use a module, too, but if you want/need to know how the math works, it's actually pretty simple:

Update: Add this summary of the math:

Convert IP address (or route subnet) to integer:

    my $ip = ($A << 24) + ($B << 16) + ($C << 8) + $D;
    # Do the same for each route address ($net)
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Convert /24 CIDR notation to 0xffffff00 netmask:

Check if a destination IP matches a route:

Full example:

#!/usr/bin/env perl

use 5.012;
use warnings FATAL => 'all';

# Use an array instead if order is important
my %routes = (
    '192.168.0.1' => [ '192.168.0.0' => 24 ],
    '10.10.10.1'  => [ '10.10.10.0'  => 24 ],
    'default'     => [ '12.162.8.11' => 28 ],
);

printf "%15s -> %s\n", $_, route($_)
    for qw< 10.10.10.12 128.127.126.125 192.168.0.51
            192.168.1.1 10.10.10.5 >;

sub ip {
    $_[0] =~ /^(\d+)\.(\d+)\.(\d+)\.(\d+)$/ or die "Invalid IP";
    die "Octet out of range" if ($1 & $2 & $3 & $4) > 255;
    ($1 << 24) + ($2 << 16) + ($3 << 8) + $4
}

sub route {
    my $ip = ip($_[0]);
    while (my ($dest, $route) = each %routes) {
        my ($net, $cidr) = @$route;
        my $mask = 0xffffffff ^ (1 << 32 - $cidr) - 1;
        return $dest if ($ip & $mask) == ip($net);
    }
    return 'default';
}
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Output:

    10.10.10.12 -> 10.10.10.1
128.127.126.125 -> default
   192.168.0.51 -> 192.168.0.1
    192.168.1.1 -> default
     10.10.10.5 -> 10.10.10.1
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