Question

you are a high school student tasked with designing a scale model of a new playground for a day care center. the actual playground will be 50 meters long and 30 meters wide. you need to create a smaller scale model that fits within the dimensions of a 1 - meter by 1 - meter display board.
what is the largest scale factor you could use that would allow the entire playground to fit on the display board?
use the keypad to enter your answer.
the largest scale factor that allows the model to fit on the display board is

Explanation:

Step1: Calculate scale factor for length

The actual length is \(50\) meters and the display board length is \(1\) meter. The scale factor for length \(s_{l}=\frac{1}{50}\)

Step2: Calculate scale factor for width

The actual width is \(30\) meters and the display board width is \(1\) meter. The scale factor for width \(s_{w}=\frac{1}{30}\)

Step3: Determine the largest scale factor

Since \(\frac{1}{50}= 0.02\) and \(\frac{1}{30}\approx0.033\), the smaller of the two scale - factors will ensure both dimensions fit.

Answer:

\(0.02\)