Particular 11591

The particular map has a scale of 1:75000
a) The distance between the two places on the map is 42mm. What is the actual distance?
b) How long would the distance show, 15.75 km on the map?

Correct answer:

a =  3.15 km
b =  21 cm

Step-by-step explanation:

$$\begin{gathered} k=75000 \\ A=4.2\text{cm}\to \text{km}=4.2:100000\text{km}=4.0\cdot 10^{-5}\text{km} \\ a=A\cdot k=4.2\cdot 10^{-5}\cdot 75000=\frac{63}{20}\text{km}=3.15\text{km} \end{gathered}$$

$$\begin{gathered} B=15.75\text{km}\to \text{cm}=15.75\cdot 1000\cdot 100\text{cm}=1575000\text{cm} \\ b=B/k=1575000/75000=21\text{cm} \end{gathered}$$

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