OG详解-OG4 数学2 Q26

Choice B is correct. Let x represent the side length, in cm, of each square base.   If the two prisms are glued together along a square base, the resulting prism has a surface area equal to twice the surface area of one of the prisms, minus the area of the two square bases that are being glued together, which yields 2K -2x² cm2.  It’s given that this resulting surface area is equal to K 9247​​ cm² , so 2K -2x²  = 9247K . Subtracting 9247​​ K from both sides of this equation yields 2K - 9247​​K -2x²= 0. This equation can be rewritten by multiplying 2K on the left-hand side by 47​47, which yields 94​47​ K - 9247K -2x² = 0, or 2​47​ K -2x² = 0. Adding 2x² to both sides of this equation yields 2​47​ K = 2x². Multiplying both sides of this equation by47​2​ yields K = 47x². The surface area K, in cm², of each rectangular prism is equivalent to the sum of the areas of the two square bases and the areas of the four lateral faces. Since the height of each rectangular prism is 90 cm and the side length of each square base is x cm, it follows that the area of each square base is  x² cm²  and the area of each lateral face is  90x cm². Therefore, the surface area of each rectangular prism can be represented by the expression  2x² +4 (90x), or 2x² +360x. Substituting this expression for K  in the equation K = 47x² yields  2x² +360x = 47x^2. Subtracting 2x² and 360x from both sides of this equation yields 0 = 45x² -360x. Factoring x  from the right-hand side of this equation yields 0 = x (45x -360). Applying the zero product property, it follows that x = 0 and 45x -360 = 0. Adding 360  to both sides of the equation 45x -360 = 0 yields 45x = 360 . Dividing both sides of this equation by 45 yields x = 8. Since aside length of a rectangular prism can’t be  0, the length of each square base is 8 cm.
Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.