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: Find the scale factor

Given the scale \(3\ cm:1.5\ km\). To find the number to multiply the scale - drawing distance by, we need to find out how many kilometers correspond to \(1\ cm\) in the scale drawing.
We use the formula for scale: if \(3\ cm\) represents \(1.5\ km\), then let \(x\) be the actual distance (in km) for \(1\ cm\) in the drawing.
We set up the proportion \(\frac{3\ cm}{1.5\ km}=\frac{1\ cm}{x}\).
Cross - multiply: \(3x = 1.5\).
Solve for \(x\): \(x=\frac{1.5}{3}\).

Step2: Calculate the value of \(x\)

\(x = 0.5\)

Answer:

\(0.5\)