The plan

The plan of the housing estate is on 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 answer:

x₁ =  24 cm
x₃ =  8 cm
s₂ =  1.2 km

Step-by-step explanation:

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

$x_3=s/m_3=120000/15000=8\text{cm}$

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

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