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
Explanation:
Area of the sheet left unpainted is two-thirds of painted area i.e., area of the circles will be three-fifth of the total area.
∴ Area of the circle = 3/5 × 135 = 54 sq. in.
Let the radius of the circle be r and l be the length of the rectangle. Width of the rectangle will be 2r.
⇒ πr2 = 81
⇒ r = 9π
Area of rectangle = 135 = 2r × l
⇒ l = 1352r = 1352×9π = 15π2
∴ Perimeter of the rectangle = 2(l + r) = 215π2+18π = 3π5 +12π
Hence, option (c).
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