Differentiation - Problems Involving Maximisation and Minimisation

The diagram shows a river of \(\sqrt{5}\) km in width, where village \(B\) is \(5\) km downstream from village \(A\). A bridge and a road are to be built to connect the two villages. It is known that the cost of building a bridge to that of building a road of the same length is \(3 : 2\). Assume that the bridge will be built from village \(A\) to a point \(C\), \(x\) km from a point \(D\) directly opposite to village \(A\) across the river, and the road will be built from \(C\) to village \(B\).

1. Find, respectively, the lengths of the bridge and of the road in terms of \(x\).
2. Find the value of \(x\) for which the total cost of building the bridge and the road has a minimum value.