Question

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 picnic area trail? km 3 cm : 1.5 km

Explanation:

Step1: Find the scale - factor

Given the scale $3\ cm:1.5\ km$, we first convert the units so that they are the same. Since $1\ km = 100000\ cm$, $1.5\ km=1.5\times100000 = 150000\ cm$. The scale - factor $k$ is found by dividing the actual distance by the scale - drawing distance. For the given scale $3\ cm$ (scale - drawing) and $150000\ cm$ (actual), $k=\frac{150000}{3}=50000$. Another way is to note that if we rewrite the scale as a ratio $\frac{1.5\ km}{3\ cm}=0.5\ km/cm$. So we multiply each distance in the scale drawing by $0.5$ (in km per cm) to get the actual distance.

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

The length of the picnic - area trail in the scale drawing is $9\ cm$. To find the actual length $L$, we use the scale relationship. Since we multiply the scale - drawing length by the scale - factor (in km per cm), $L = 9\times0.5=4.5$ km.

Answer:

4.5