Question

a rectangular prism has a length of 4.2 cm, a width of 5.8 cm, and a height of 9.6 cm. a similar prism has a length of 14.7 cm, a width of 20.3 cm, and a height of 33.6 cm. the dimensions of the smaller prism are each multiplied by what factor to produce the corresponding dimensions of the larger prism? \\( 3\frac{1}{2} \\) \\( 4 \\) \\( 4\frac{5}{6} \\) \\( 5 \\)

Explanation:

Step1: Divide larger length by smaller length

To find the scale factor, we divide the length of the larger prism by the length of the smaller prism. The length of the larger prism is \(14.7\) cm and the length of the smaller prism is \(4.2\) cm. So we calculate \(\frac{14.7}{4.2}\).
\[
\frac{14.7}{4.2}=3.5
\]

Step2: Convert 3.5 to a mixed number

We know that \(3.5 = 3+\frac{1}{2}=3\frac{1}{2}\). We can also check with the other dimensions (width and height) to confirm. For width: \(\frac{20.3}{5.8} = 3.5=3\frac{1}{2}\), and for height: \(\frac{33.6}{9.6}=3.5 = 3\frac{1}{2}\). So the scale factor is \(3\frac{1}{2}\).

Answer:

\(3\frac{1}{2}\) (corresponding to the option with \(3\frac{1}{2}\))