Question

A topographical map extract drawn at a scale of $1:50,000$ delineates a drainage basin. The total area of the basin measured on the map is $160\text{ cm}^2$. Morphometric analysis reveals the following total stream segment lengths measured directly from the map across all stream orders:
- 1st-order stream segments: $48\text{ cm}$
- 2nd-order stream segments: $20\text{ cm}$
- 3rd-order stream segments: $12\text{ cm}$
- 4th-order stream segments: $8\text{ cm}$

Calculate the drainage density of the river basin in $\text{km/km}^2$.