A window is in the form of a rectangle surmounted by an equilateral triangle on its length. Let the rectangular part have length and breadth $x$ and $y$ metres respectively. Based on the given information, answer the following questions : (i) If the perimeter of the window is $12\text{ m}$, find the relation between $x$ and $y$. (ii) Using the expression obtained in (i), write an expression for the area of the window as a function of $x$ only. (iii) (a) Find the dimensions of the rectangle that will allow maximum light through the window. (use expression obtained in (ii)) OR (iii) (b) If it is given that the area of the window is $50\text{ m}^2$, find an expression for its perimeter in terms of $x$.