A circle is inscribed in a square. If the difference between area of the square and circle is 262.5 cm⊃2;, then find the area of the rectangle whose perimeter is same as that of circle while length of rectangle is 20% more than the breadth of rectangle (in cm⊃2;).
Answer: D
Let the side of square be 2a.
So, the diameter of circle = 2a
Radius of circle = a
WKT, Area of square = 4a
Area of circle = π r⊃2;
Perimeter of circle = 2π r
Area of rectangle = l x b
Perimeter of rectangle = 2(l + b)
Given that difference between area of the square and circle is 262.5 cm⊃2;.
Area of square - Area of circle = 262.5
4a⊃2; - (22/7)a⊃2; = 262.5
28a⊃2; - 22a⊃2; = 1837.5
6a⊃2; = 1837.5
a⊃2; = 306.25
a = 17.5 cm
Perimeter of circle = 2πa = 2 x (22/7) x 17.5 = 110 cm
Also given length of rectangle is 20% more than the breadth of rectangle.
Let the breadth of rectangle be X.
So, length of rectangle = (120/100)X = 1.2X
As per the question,
Perimeter of rectangle = Perimeter of circle
2(1.2X + X) = 110
2.4X + 2X = 110
4.4X = 110
X = 25 cm
Breadth of rectangle = 25 cm
Length of rectangle = 1.2(25) = 30 cm
Area of rectangle = 25 x 30 = 750 cm⊃2;.