Two identical rectangular prisms each have a height of $90 \text{centimeters} \left(\text{cm}\right)$. The base of each prism is a square, and the surface area of each prism is $K {\text{cm}}^2$. If the prisms are glued together along a square base, the resulting prism has a surface area of $\frac{92}{47}K {\text{cm}}^2$. What is the side length, in $\text{cm}$, of each square base?