Sixth pairwise product of four positive reals

Four positive real numbers $a,b,c,d$ are multiplied in all $6$ possible pairs, and the six products are exactly $9,10,12,27,30$ and some unknown $x$. Determine $x$.

$\tfrac{45}{2}$. The ratios $9:10$ and $27:30$ suggest two numbers in ratio $9:10$ each multiplied by two other numbers. Taking $c=2$, $d=6$ gives $a=\tfrac92$, $b=5$, which produces $9,10,27,30$ and $cd=12$. The remaining product is $ab=\tfrac92\cdot5=\tfrac{45}{2}$.