To analyze the relationship between the surface areas and dimensions of the prisms, we need to consider how surface area relates to the dimensions of a rectangular prism.
The surface area \( S \) of a rectangular prism with dimensions \( l \), \( w \), and \( h \) is given by the formula:
\[ S = 2(lw + lh + wh) \]
Now, prism A has a surface area of 25 square units, and prism B has a surface area of 100 square units. We can see that:
\[ \frac{S_B}{S_A} = \frac{100}{25} = 4 \]
This means that the surface area of prism B is 4 times that of prism A.
When comparing the dimensions of two similar geometric shapes, the ratio of their dimensions is the square root of the ratio of their surface areas:
\[ \text{ratio of dimensions} = \sqrt{\frac{S_B}{S_A}} = \sqrt{4} = 2 \]
This indicates that the dimensions of prism B are 2 times the dimensions of prism A.
Therefore, the accurate 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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