To analyze the relationship between the surface areas and dimensions of the rectangular prisms, we need to understand how surface area scales with dimensions.
The surface area \( S \) of a rectangular prism is given by the formula: \[ S = 2(ab + bc + ac) \] where \( a \), \( b \), and \( c \) are the dimensions of the prism. If the dimensions of prism A are \( a, b, c \), the surface area is \( S_A = 25 \). For prism B, if its dimensions are \( k \cdot a, k \cdot b, k \cdot c \), the surface area becomes: \[ S_B = 2((k a)(k b) + (k b)(k c) + (k a)(k c)) = 2k^2(ab + bc + ac) = k^2 \cdot S_A \] This shows that if we want the surface area of prism B to be 4 times that of prism A, we need to solve: \[ k^2 \cdot S_A = 4 \cdot S_A \] Thus, \[ k^2 = 4 \] This means that \( k = 2 \).
The dimensions of prism B are therefore twice as large as the dimensions of prism A.
The correct option is: B. Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are twice as large as prism A’s.
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