The sum of circumference of a circle and perimeter of a rectangle is 480 cm. If the area of the rectangle is 168 cm² and ratio of radius of the circle and breadth of the rectangle is 19:2. Find the area of another circle whose radius is 28% of the diagonal of rectangle. (Note – Length and Breadth of rectangle must be integer) 1) 343 cm² 2) 230 cm² 3) 350 cm² 4) 154 cm² 5) 189 cm²

• Area of the rectangle = 168 cm2
  Ratio of radius of the circle and breadth of the rectangle = 19 : 2
  Let the radius of the circle be 19x and breadth of the rectangle be 2x.
  WKT, Area of rectangle = l*b
  l*b = 168
  l*2x = 168
  l = 84/x cm
  Circumference of a circle = 2π r
  Perimeter of rectangle = 2(l + b)
  Sum of circumference of a circle and perimeter of a rectangle = 480 cm
  2π r + 2(l + b) = 480
  2*(22/7)*19x + 2[(84/x) + 2x] = 480
  36x2 - 140x + 49 = 0
  x = 7/2
  So, breadth of rectangle = 2(7/2) = 7 cm
  length of rectangle = 84/(7/2) = 24 cm
  Diagonal of rectangle = √[242 + 72]
  = √[576 + 49]
  = √625
  = 25 cm
  Let the radius of new circle be 'R'.
  Radius of new circle is 28% of the diagonal of rectangle = (28/100)*25
  = 7 cm.
  Area of new circle = π R2
  = (22/7)*(7)2
  = 154 cm2.
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