The length of the transverse axis of the rectangular hyperbola $xy=18$ is: 

The given equation of rectangular hyperbola is $xy = 18 \dots \dots \dots \dots \left(i\right)$On comparing Eq. (i), with general equation of rectangular hyperbola $xy=\frac{a^2}{2}$
We get,  $\frac{a^2}{2}=18\Rightarrow a^2=36\Rightarrow a=6$
 Length of the transverse axis of rectangular hyperbola is $2a = 2 x 6 = 12$