Question

what number can you multiply each distance in the scale drawing by to find the actual distance? 0.5 what is the actual length of the picnic area trail? km

Explanation:

Step1: Find the scale factor

Given the scale \(3\ cm:1.5\ km\). To find the number to multiply the scale - drawing distance by, we first simplify the ratio.
We know that if \(3\ cm\) represents \(1.5\ km\), then for \(1\ cm\) in the scale - drawing, the actual distance \(d\) is given by the proportion \(\frac{3\ cm}{1.5\ km}=\frac{1\ cm}{d}\). Cross - multiplying gives \(3d = 1.5\), so \(d=\frac{1.5}{3}=0.5\ km/cm\).

Step2: Calculate the actual length of the picnic area trail

The length of the picnic area trail in the scale - drawing is \(9\ cm\).
Using the scale factor \(0.5\ km/cm\), the actual length \(L\) of the picnic area trail is \(L=\text{scale - drawing length}\times\text{scale factor}\).
Substitute the values: \(L = 9\ cm\times0.5\ km/cm\).

Answer:

\(4.5\)