The ratio compares two things. The length of the trail, in reality, is 6.75 km.
A scaling ratio helps us to compare two things.
Given to us
The scale on the map states that 2 centimeters represent 3 kilometers.
Length of the trail on the map, L = 4.5 cm = 0.045 m
As we know that 2 centimeters represent 3 kilometers. therefore,
[tex]\rm \dfrac{Map }{Real}=\dfrac{0.02}{3000}[/tex]
We know that the Length of the trail on the map is 0.045 m,
[tex]\rm \dfrac{L}{L'} =\dfrac{0.02}{3000}[/tex]
Substitute the values,
[tex]\rm \dfrac{0.045}{L'}=\dfrac{0.02}{3000}\\\\L' = \dfrac{0.045 \times 3000}{0.02}\\\\L' = 6750 \ m \\\\L' =6.750\ km[/tex]
Hence, the length of the trail, in reality, is 6.75 km.
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