Question

chaya 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: Convert units

We know that \(1\ km = 100000\ cm\). So \(1.5\ km=1.5\times100000 = 150000\ cm\).

Step2: Find the scale factor

The scale is \(3\ cm:1.5\ km\). Substitute \(1.5\ km = 150000\ cm\) into the scale. Let the scale factor be \(k\). We have the proportion \(\frac{3}{150000}=\frac{1}{k}\). Solving for \(k\), we get \(k = 50000\).

Answer:

\(50000\)