So, my questions: (1) how do I build this variable $type.$t and (2) is there a better way?

The usual response when someone wants to do this is (and it applies equally here) use a hash.

$t = $q->param('type');
$type{$t} = 1;
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That said, if you *really* want to create variables "the evil way", it's done like this:

If $type = 5, then this will create a variable called $type5 and give it a value of 1. Caveat lector!