A map of a nature reserve is set to a scale of $1:n$, where $n$ is a whole number. A forest

Question

A map of a nature reserve is set to a scale of $1:n$, where $n$ is a whole number. A forest block with an area of $1$ $\mathrm{km}^2$ is represented by $4$ $\mathrm{cm}^2$ on the map.

Find the value of $n$.

A new map is drawn for the same area, such that the area of the forest block on the original map is $9$ times as large as the area represented on the new map.

Calculate the real-world distance, in $\mathrm{km}$, represented by $12$ cm on this new map.

Accepted Answer

(a) $n=50\,000$. (b) $18$ km.

Congruence and Similarity - Map Scales

Congruence and Similarity - Map Scales

Solution:

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