A farmer wishes to grow a \(150\ m^2\) rectangular kitchen garden. Since he has only \(40\ m\) of barbed wire, he fences three sides of the kitchen garden, using the compound wall of his houses as the fourth side.
(i) Represent the given problem in quadratic form.
(ii) Find the dimensions of the garden.
(iii) Calculate the perimeter of the garden if all four sides were fenced.
(iv) Suppose the farmer fences all the four side of a garden, the cost of fencing all four sides at \(₹\ 50\) per meter is \(₹\) _______.