Discussion
A circle is inscribed in a square. If the difference between area of the square and circle is 262.5 cm², 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 cm²).
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 r²
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 cm².
Area of square - Area of circle = 262.5
4a² - (22/7)a² = 262.5
28a² - 22a² = 1837.5
6a² = 1837.5
a² = 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 cm².
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