To determine how the dimensions of rectangular prism B compare to those of rectangular prism A based on their surface areas, we can first analyze the relationship between surface area and dimensions.
The surface area \( S \) of a rectangular prism is given by the formula:
\[ S = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the length, width, and height of the prism, respectively.
If the surface area of prism A is 25 square units and the surface area of prism B is 100 square units, then:
\[ \frac{S_B}{S_A} = \frac{100}{25} = 4 \]
This means prism B has a surface area four times that of prism A.
However, when comparing dimensions, we need to remember that if the surface area of one prism is \( k^2 \) times that of another prism, then the linear dimensions are scaled by a factor of \( k \).
In this case, since the surface area of prism B is 4 times that of prism A, we can take the square root to find the scale factor for the dimensions:
\[ k = \sqrt{4} = 2 \]
This means that the dimensions of prism B are twice as large as the dimensions of prism A, not half or eight times as large.
The correct response 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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