Scale

The swimming pool is long 50 m and 30 m wide. The city's plan is shown as a rectangle with an area 2.4 cm².

What scale is the city plan?

Final Answer:

M =  1:2500

Step-by-step explanation:

$$\begin{gathered} a=50\text{m} \\ b=30\text{m} \\ {S}_1=2.4{\text{cm}}^2\to {\text{m}}^2=2.4:10000{\text{m}}^2=0.00024{\text{m}}^2 \\ {S}_2=a\cdot b=50\cdot 30=1500{\text{m}}^2 \\ k=S_1/S_2=0.0002/1500\doteq 1.6\cdot 10^{-7} \\ {M}^2=k \\ M=\sqrt{k}=\sqrt{1.6\cdot 10^{-7}}=0.0004=1:2500 \end{gathered}$$

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