Question

chey has a map that shows the lengths of some hiking trails. the scale is shown in the drawing. what number can you multiply each distance in the scale - drawing by to find the actual distance? ?

Explanation:

Step1: Identify scale - factor concept

The scale of the map is given as \(3\ cm = 1.5\ km\). To find the factor to multiply map - distances by to get actual distances, we first need to find out how many kilometers are represented by \(1\ cm\) on the map.
We know that if \(3\ cm\) represents \(1.5\ km\), then for \(1\ cm\), we set up a proportion. Let \(x\) be the actual distance in kilometers for \(1\ cm\) on the map. So \(\frac{1.5}{3}=\frac{x}{1}\).

Step2: Solve for \(x\)

\(x=\frac{1.5}{3}=0.5\ km\) per \(cm\). So to convert a distance \(d\) (in \(cm\)) on the map to the actual distance \(D\) (in \(km\)), we use the formula \(D = 0.5d\). The number we multiply each distance in the scale - drawing by is \(0.5\).

Answer:

\(0.5\)