An architect designs a building for a multi-national company. The floor consists of a rectangular region with semicircular ends having a perimeter of 200m as shown below:Based on the above information answer the following:(i) If x and y represents the length and breadth of the rectangular region, then the relation between the variables is a) x + πy = 100b) 2x + πy = 200 c) πx + y = 50 d) x + y = 100(ii) The area of the rectangular region A expressed as a function of x is a) \(\frac{2}{\pi}\) (100x − x2) b) \(\frac{1}{\pi}\) (100x − x2) c) \(\frac{x}{\pi}\) (100 − x) d) πy2 + \(\frac{2}{\pi}\)(100x − x2) (iii) The maximum value of area A isa) \(\frac{\pi}{3200}m^2\)b) \(\frac{3200}{\pi}m^2\)c) \(\frac{5000}{\pi}m^2\)d) \(\frac{1000}{\pi}m^2\)(iv) The CEO of the multi-national company is interested in maximizing the area of the whole floor including the semi-circular ends. For this to happen the valve of x should be a) 0 m b) 30 m c) 50 m d) 80 m(v) The extra area generated if the area of the whole floor is maximized is : a) \(\frac{3000}{\pi}m^2\)b) \(\frac{5000}{\pi}m^2\)c) \(\frac{7000}{\pi}m^2\)d) No change Both areas are equal