# 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:

$m_{1}=5000 \ \\ m_{2}=10000 \ \\ m_{3}=15000 \ \\ \ \\ x_{2}=12 \ \text{cm} \ \\ \ \\ s=x_{2} \cdot \ m_{2}=12 \cdot \ 10000=120000 \ \text{cm} \ \\ \ \\ x_{1}=s/m_{1}=120000/5000=24 \ \text{cm}$
$x_{3}=s/m_{3}=120000/15000=8 \ \text{cm}$
$s_{1}=s \rightarrow m=s / 100 \ m=120000 / 100 \ m=1200 \ m \ \\ s_{2}=s_{1} \rightarrow km=s_{1} / 1000 \ km=1200 / 1000 \ km=1.2 \ km=\dfrac{ 6 }{ 5 }=1.2 \ \text{km}$

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