2025 AHS PRELIMS P1 Q16

Map \(A\) has a scale of \(1:200\,000\) and map \(B\) has a scale of \(1:n\). The area of a lake on map \(A\) is \(4\text{ cm}^2\) while the area of the same lake on map \(B\) is \(2.56\text{ cm}^2\). Find \(n\).[3]