Short Answer 
The solution begins by defining the side length of squares as ‘s’ and setting up surface area equations for a rectangular prism. After deriving and simplifying the equations, the side length is found to be ‘s = 8 cm.’
Step 1: Define the Variables
Start by letting s represent the side length of each square. This variable will be essential for all calculations involving the surface area of the rectangular prism. Understanding the problem setup is crucial as we’ll work through equations to derive s.
Step 2: Set Up the Surface Area Equations
Use the formula for the surface area of the rectangular prism, which can be expressed as 360·s + 2·s². Additionally, for prisms glued along a square base, the surface area becomes 720·s + 2·s². Establish the equations as follows:
- Equation (1): 720·s + 2·s² = (92/47)·k
- Equation (2): 360·s + 2·s² = k
Step 3: Solve for Side Length
With both equations established, subtract Equation (2) from Equation (1) to eliminate k and consolidate terms involving s. This leads to:
- 360·s = (45/47)·k
- Rearranging gives 2¬∑s¬≤ Р16¬∑s = 0
Factoring results in 2¬∑s(s Р8) = 0, yielding s = 8 cm as the solution for the side length of the square.