Similar Figures and Surface Area Quick Check 2 of 52 of 5 Items Question Rectangular prism A has a surface area of 25 square units and rectangular prism B has a surface area of 100 square units. Which statement accurately compares the dimensions of prism A to those of prism B ?(1 point) Responses Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are half as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are half as large as prism upper A ’s. Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are 8 times as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are 8 times as large as prism upper A ’s. Since prism B’s surface area is 4 times as large as prism A’s surface area, prism B’s dimensions are 16 times as large as prism A’s. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are 16 times as large as prism upper A ’s. 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. Since prism upper B ’s surface area is 4 times as large as prism upper A ’s surface area, prism upper B ’s dimensions are twice as large as prism upper A ’s. Skip to navigation page 17 of 17 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To compare the dimensions of the rectangular prisms A and B based on their surface areas, we can utilize the relationship between the surface area and the dimensions of similar figures.

The surface area of a three-dimensional shape (such as a rectangular prism) is proportional to the square of its linear dimensions. This means that if the surface area of prism B is 4 times that of prism A, we can deduce the ratio of their dimensions.

Let’s denote the dimensions of prism A as \(d_A\) and the dimensions of prism B as \(d_B\).

Given:

• Surface area of prism A = 25 square units
• Surface area of prism B = 100 square units

Since \(100 = 4 \times 25\), we can find the ratio of the dimensions:

\[ \left( \frac{d_B}{d_A} \right)^2 = 4 \]

Taking the square root of both sides gives:

\[ \frac{d_B}{d_A} = 2 \]

This implies that each dimension of prism B is twice that of prism A.

Thus, 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."

This statement aligns with the proportional relationship we derived.