if( $string=~/ ^ $myvar REC: (.*) /x )
Also, Mind the meta!, that means if your $myvar contains any characters like the dot (.) and you don't want these to be interpreted as regex special characters, or any whitespace in the variable to be ignored under /x, then you need to wrap your string in \Q...\E (see also quotemeta):
if( $string=~/ ^ \Q$myvar\E REC: (.*) /x )
Update: Added links to docs. Also added bit about whitespace in the variable under /x.
Update 2: Just to be clear, I recommend you always use \Q...\E, even if you don't use /x, unless you specifically want regex metacharacters in $myvar to be treated as such and it comes from a trusted source! That is, if($string=~/^\Q$myvar\EREC:(.*)/)