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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 - 2 2 of the two square bases that are being glued together, which yields 2K 2x cm . 92 2 - 2=92 It’s given that this resulting surface area is equal to K cm , so 2K 2x K. 47 47 92 -92 - 2= Subtracting K from both sides of this equation yields 2K K 2x 0. This 47 47 47 equation can be rewritten by multiplying 2K on the left-hand side by , which 47 94 -92 - 2= 2 - 2= 2 yields K K 2x 0, or K 2x 0. Adding 2x to both sides of this 47 47 47 2 = 2 47 equation yields K 2x . Multiplying both sides of this equation by yields 47 2 = 2 2 K 47x . The surface area K, in cm, of each rectangular prism is equivalent to the sum of the areas of the two square bases and the areas of the four lateral 52 SAT PRACTICE TEST #4 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS nnn MATH: MODULE 2 faces. Since the height of each rectangular prism is 90 cm and the side length of 2 2 each square base is x cm, it follows that the area of each square base is x cm 2 and the area of each lateral face is 90x cm . Therefore, the surface area of each 2+ ( ) rectangular prism can be represented by the expression 2x 4 90x , or 2+ = 2 2x 360x. Substituting this expression for K in the equation K 47x yields 2+ = 2 2 2x 360x 47x . Subtracting 2x and 360x from both sides of this equation = 2- yields 0 45x 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 a side 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.