To analyze the relationship between the surface areas of the two rectangular prisms (A and B) and their dimensions, we can use the formula for the surface area of a rectangular prism, which is:
\[ SA = 2(lw + lh + wh) \]
where \(l\), \(w\), and \(h\) are the length, width, and height of the prism.
The surface area of prism A is 25 square units, and the surface area of prism B is 100 square units. We observe that:
\[ \frac{SA_B}{SA_A} = \frac{100}{25} = 4 \]
This tells us that prism B's surface area is 4 times that of prism A.
When the dimensions of a three-dimensional object are scaled by a factor \(k\), the surface area scales by a factor of \(k^2\). Therefore, if the dimensions of prism B are \(k\) times larger than those of prism A, we have:
\[ \left( \frac{SA_B}{SA_A} \right) = k^2 \]
In this case, we found:
\[ 4 = k^2 \]
Solving for \(k\):
\[ k = \sqrt{4} = 2 \]
This means that the dimensions of prism B are 2 times as large as the corresponding dimensions of prism A.
Therefore, 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.