On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

• A. \(3\sqrt \pi \left( {5 + \frac{{12}}{\pi }} \right)\)
• B. \(3\sqrt \pi \left( {\frac{5}{2}+ \frac{{6}}{\pi }} \right)\)
• C. \(5\sqrt \pi \left( {3+ \frac{{9}}{\pi }} \right)\)
• D. \(4\sqrt \pi \left( {3 + \frac{{9}}{\pi }} \right)\)