For The Mathematically Inclined

Problem 1

Two identical rectangular prisms each have a height of 90 cm. The base of each prism is a square, and the surface area of each prism is K cm². If the prisms are glued together along a square base, the resulting prism has a surface area of 92/47 K cm². What is the side length, in cm, of each side of the square base?

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