Question

a has a map that shows the lengths of some hiking trails. the scale is shown in the drawing. number can you multiply each distance in ale drawing by to find the actual distance? s the actual length of the picnic area trail? km 3 cm:1.5 km

Explanation:

Step1: Determine the scale - factor

The scale is $3\ cm:1.5\ km$. First, convert $1.5\ km$ to $cm$. Since $1\ km = 100000\ cm$, then $1.5\ km=1.5\times100000 = 150000\ cm$. The scale - factor $k$ is $\frac{150000}{3}=50000$. So we multiply each distance on the map (in cm) by $50000$ to get the actual distance (in cm), and then convert to km.

Step2: Calculate the actual length of the picnic - area trail

The length of the picnic - area trail on the map is $9\ cm$. Multiply the map length by the scale - factor: $9\times50000 = 450000\ cm$. Convert $450000\ cm$ to km. Since $1\ km = 100000\ cm$, then $\frac{450000}{100000}=4.5\ km$.

Answer:

1. The number to multiply each distance by is $50000$.
2. The actual length of the picnic area trail is $4.5$ km.