To analyze the relationship between the surface areas of rectangular prisms A and B, we first note the given information:
- Surface Area of Prism A = 25 square units
- Surface Area of Prism B = 100 square units
We see that the surface area of prism B is 4 times that of prism A (100 / 25 = 4).
The surface area \( S \) of a rectangular prism is given by the formula: \[ S = 2(ab + ac + bc) \] where \( a \), \( b \), and \( c \) are the dimensions of the prism.
While the surface area increases with the dimensions, the relationship is not linear; instead, it's based on the square of the scaling factor of the dimensions. If the dimensions of prism A are multiplied by a factor \( k \), the surface area of prism B would be: \[ S_B = 2(k a)(k b) + 2(k a)(k c) + 2(k b)(k c) = k^2 \cdot S_A \]
Since we have determined that the surface area of prism B is \( 4 \) times that of prism A (i.e., \( k^2 = 4 \)), we can find \( k \) by taking the square root: \[ k = \sqrt{4} = 2 \]
This means that each dimension of prism B is 2 times that of prism A.
Thus, the correct statement is: 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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