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The net of a rectangular prism is shown below. The surface area of each face is labeled.On the tactile printout of the following graphs, b is 36 centimeters squared, c is 108 centimeters squared, and d is 48 centimeters squared.
36 cm²
108 cm²
48 cm²
36 cm²
48 cm²
108 cm²
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Which values represent the dimensions, in centimeters, of the rectangular prism? (Note: diagram is NOT to scale)
Answer
Multiple Choice Answers
4, comma, 36, comma, 484,36,48
4, comma, 9, comma, 124,9,12
3, comma, 12, comma, 483,12,48
36, comma, 48, comma, 10836,48,108

Answer 1

To find the dimensions of the rectangular prism based on the given surface areas of its faces, we can use the surface area formula for a rectangular prism. The surface area \(S\) is given by the formula:

\[
S = 2lw + 2lh + 2wh
\]

where \(l\), \(w\), and \(h\) are the length, width, and height of the prism.

From the information provided, we have:

- Two faces with areas of \(36 \, \text{cm}^2\)
- One face with an area of \(48 \, \text{cm}^2\)
- One face with an area of \(108 \, \text{cm}^2\)

Let's organize this based on possible pairs of dimensions from the answers provided.

1. **For the option (4, 36, 48)**:
- Dimensions would be \(l = 4, w = 36, h = 48\)
- Checking surfaces:
- \(lw = 4 \cdot 36 = 144 \, \text{cm}^2\) (not matching)

2. **For the option (4, 9, 12)**:
- Dimensions would be \(l = 4, w = 9, h = 12\)
- Checking surfaces:
- \(lw = 4 \cdot 9 = 36 \, \text{cm}^2\) (matches),
- \(lh = 4 \cdot 12 = 48 \, \text{cm}^2\) (matches),
- \(wh = 9 \cdot 12 = 108 \, \text{cm}^2\) (matches).
- This is a valid option.

3. **For the option (3, 12, 48)**:
- Dimensions would be \(l = 3, w = 12, h = 48\)
- Checking surfaces:
- \(lw = 3 \cdot 12 = 36 \, \text{cm}^2\) (matches),
- \(lh = 3 \cdot 48 = 144 \, \text{cm}^2\) (not matching).

4. **For the option (36, 48, 108)**:
- Dimensions would be \(l = 36, w = 48, h = 108\)
- \(lw\) would yield a very large area (matching not likely).

The only valid option based on surface area checks is:

**(4, 9, 12)**.

Thus, **the dimensions of the rectangular prism are 4 cm, 9 cm, and 12 cm**.