The plan

The plan of the housing estate is in three scales 1: 5000,1: 10000,1: 15000. The distance between two points on a plan with a scale of 1: 10000 is 12 cm. What is this distance on the other two plans? What is this distance?

Correct result:

x₁ =  24 cm
x₃ =  8 cm
s₂ =  1.2 km

Solution:

$$\begin{gathered} m_1=5000 \\ {m}_2=10000 \\ {m}_3=15000 \\ {x}_2=12\text{ cm } \\ s=x_2\cdot m_2=12\cdot 10000=120000\text{ cm } \\ {x}_1=s\mathrm{/}{m}_1=120000\mathrm{/}5000=24\text{ cm} \end{gathered}$$

$x_3=s\mathrm{/}{m}_3=120000\mathrm{/}15000=8\text{ cm}$

$$\begin{gathered} s_1=s\to \text{ m}=s\mathrm{/}100\text{ m}=120000\mathrm{/}100\text{ m}=1200\text{ m } \\ {s}_2=s_1\to \text{ km}=s_1\mathrm{/}1000\text{ km}=1200\mathrm{/}1000\text{ km}=1.2\text{ km}={\displaystyle \frac{6}{5}}\text{ km} \end{gathered}$$

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