To compare the dimensions of rectangular prisms A and B based on their surface areas, it’s important to understand the relationship between surface area and dimensions. The surface area \( SA \) of a rectangular prism can be expressed as:
\[ SA = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the length, width, and height of the prism.
When the dimensions of a prism are scaled by a factor \( k \), the surface area is scaled by a factor of \( k^2 \).
In this situation:
- Surface area of prism A: \( 25 \) square units
- Surface area of prism B: \( 100 \) square units
The ratio of the surface areas is:
\[ \frac{SA_B}{SA_A} = \frac{100}{25} = 4 \]
This indicates that prism B’s surface area is 4 times that of prism A.
To find the relationship between their dimensions, since the surface area is scaled by a factor of 4, we need to take the square root of 4 to find the scaling factor for the dimensions:
\[ k = \sqrt{4} = 2 \]
Thus, if prism B’s surface area is 4 times that of prism A’s, then the dimensions of prism B are 2 times as large as those of prism A.
Therefore, the accurate statements from the options provided are:
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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