Question

determining a scale factor
finding scale factor and dimensions of real - world models
consider this scaled figure of a swimming pool. the
dimensions of the original pool are 24 feet wide by 36
feet long.
use the measurements of the original and of the scaled
figure to find the scale factor and the missing length.
what is the scale factor?
what is the missing length of the scale model?

Explanation:

Step1: Calculate the scale factor

The scale factor \(k\) is the ratio of the corresponding sides of the scaled figure to the original figure. For the width, original width \(W_{original}=24\) feet and scaled width \(W_{scaled} = 6.4\) feet.

$$k=\frac{W_{scaled}}{W_{original}}=\frac{6.4}{24}=\frac{64}{240}=\frac{4}{15}$$

Step2: Find the missing length

The original length \(L_{original}=36\) feet. Using the formula \(L_{scaled}=k\times L_{original}\)

$$L_{scaled}=\frac{4}{15}\times36=\frac{4\times36}{15}=\frac{144}{15}=9.6$$

Answer:

The scale factor is \(\frac{4}{15}\) and the missing length of the scale model is \(9.6\) feet.