Quantitative Aptitude – Geometry – Circle – On a rectangular metal sheet of area 135 sq in


Slot – 1 – Quantitative Aptitude – Geometry – Circle – On a rectangular metal sheet of area 135 sq in


Q. 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?
  1. 3√π(5+12/π)
  2. 5√π(3+9/π)
  3. 4√π(3+9/π)
  4. 3√π(5/2+6/π)

Answer: 3√π(5+12/π)

Solutions:
Let the length of rectangle be l and width be 2b then 2lb =135
Also area painted /area unpainted = 3/2
Thus area painted = 3/5*135 = 81
Or πb^2=81-→b =9/√π
2lb=135 or l=135/2b= 15√π/2
So perimeter = 2l+4b = 2(l+2b) = 2 { 15√π 1/2+18/√π}= 3√π (5+12/π)


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