To compare the dimensions of rectangular prisms A and B based on their surface areas, we need to understand how surface area relates to dimensions.
The surface area \( S \) of a rectangular prism with dimensions \( l \), \( w \), and \( h \) is given by the formula:
\[ S = 2(lw + lh + wh) \]
If the surface area of prism B is 4 times that of prism A, we can represent this mathematically as:
\[ S_B = 4S_A \]
Given:
- \( S_A = 25 \) square units
- \( S_B = 100 \) square units
From the given information, it's clear that the surface area of prism B is indeed 4 times that of prism A (100 = 4 * 25).
However, to determine how the dimensions relate to each other, we need to analyze the scaling factor.
If we denote the dimensions of prism A as \( (l, w, h) \), then the dimensions of prism B can be represented as \( (k \cdot l, k \cdot w, k \cdot h) \) for some scaling factor \( k \). The new surface area would then be:
\[ S_B = 2(k \cdot l)(k \cdot w) + 2(k \cdot l)(k \cdot h) + 2(k \cdot w)(k \cdot h) \]
This can be simplified to:
\[ S_B = k^2 \cdot S_A \]
Given that \( S_B = 4S_A \), we set up the equation:
\[ k^2 \cdot S_A = 4S_A \]
Assuming \( S_A \) is not zero, we can divide both sides by \( S_A \):
\[ k^2 = 4 \]
Taking the square root:
\[ k = 2 \]
This shows that each dimension of prism B is actually twice the dimension of prism A.
Thus, the correct statement comparing the dimensions of prism A to those of prism B 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.