Congruence and Similarity - Map Scales

The scales of maps \(A\) and \(B\) are \(\frac{1}{m}\) and \(\frac{1}{n}\) respectively. A river measures \(14\) cm and \(18\) cm long respectively on maps \(A\) and \(B\). Find the ratio \(m:n\).

1. If \(0.5\) cm represents a length of \(2.5\) m on map \(A\), calculate the actual distance of the river.
2. Given that \(n=2800\) and the actual area of a sports centre is \(4212\) \(\mathrm{m}^2\), find the area of the sports centre on map \(A\).

Treat parts (a) and (b) as independent scenarios with the common ratio \(m:n\). Part (a) implies \(m=500\), whereas part (b) implies \(m=3600\); the two additional scale conditions cannot hold simultaneously.