Well johngg is right to point you to the scrolled widget. However, if you really need to make your own scrollbar ( there are certain times you may need to do it), it is easier with pack than place. With pack you tell the scrollbar to fill in it's direction, like

$yscroll->pack( -side => 'left', -fill => 'y' );
$xscroll->pack( -side => 'bottom', -fill => 'x' );
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I don't see 'fill' as an option to Tk::place, but if you read perldoc Tk::place, there are some options you can play with to try and make it the same size as the listbox, I would try the -relheight and -relwidth options. But pack is so much easier to use than place, so unless you need it for some reason, switch to pack, or use the Scrolled('Listbox'...)