To determine the factors by which the dimensions of the smaller rectangular prism were multiplied to obtain the dimensions of the larger rectangular prism, we need to find the ratio of each corresponding dimension of the larger prism to the smaller prism.
1. Calculate the Length Factor:
We are given:
- Smaller prism length: [tex]\( 4.2 \, \text{cm} \)[/tex]
- Larger prism length: [tex]\( 14.7 \, \text{cm} \)[/tex]
The factor for the length is:
[tex]\[
\frac{14.7}{4.2} = 3.5
\][/tex]
2. Calculate the Width Factor:
We are given:
- Smaller prism width: [tex]\( 5.8 \, \text{cm} \)[/tex]
- Larger prism width: [tex]\( 20.3 \, \text{cm} \)[/tex]
The factor for the width is:
[tex]\[
\frac{20.3}{5.8} = 3.5
\][/tex]
3. Calculate the Height Factor:
We are given:
- Smaller prism height: [tex]\( 9.6 \, \text{cm} \)[/tex]
- Larger prism height: [tex]\( 33.6 \, \text{cm} \)[/tex]
The factor for the height is:
[tex]\[
\frac{33.6}{9.6} = 3.5
\][/tex]
In this calculation, each dimension of the smaller prism is multiplied by the factor [tex]\( 3.5 \)[/tex] to produce the corresponding dimension of the larger prism.
Therefore, the multiplication factor for each dimension is:
[tex]\[
3 \frac{1}{2}
\][/tex]
The correct answer is [tex]\( 3 \frac{1}{2} \)[/tex].
