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?
0.5
what is the actual length of the waterfall trail?
3 cm : 1.5 km
km

Explanation:

Step1: Determine the scale factor

The scale is \(3\ cm:1.5\ km\). To find the number to multiply by, we first simplify the scale. Divide both sides of the ratio \(3\ cm:1.5\ km\) by \(3\). So, \(1\ cm=\frac{1.5}{3}\ km = 0.5\ km\).

Step2: Calculate the actual length of the waterfall trail

The length of the waterfall trail on the map is \(6\ cm\). Since \(1\ cm\) on the map represents \(0.5\ km\) in actual distance, we use the formula \(actual\ distance=map\ distance\times scale\ factor\). Substitute \(map\ distance = 6\ cm\) and \(scale\ factor=0.5\ km/cm\). Then \(actual\ distance=6\times0.5\ km\).

Answer:

The number to multiply each distance in the scale drawing is \(0.5\). The actual length of the waterfall trail is \(3\ km\).