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A Semi-circle is formed along the diagonal of rectangle. The length of rectangle is twice its breadth which is a units. Find the Ratio between Area of semi-circle and the area of rectangle.1. 55 : 282. 55 : 143. 56 : 554. 55 : 56 |
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Answer» Correct Answer - Option 4 : 55 : 56 Given: Breadth of rectangle = a Length of rectangle = 2a Semi-circle is drawn on the diagonal of rectangle. Formulas Used: Area of rectangle = Length × breadth Diagonal of rectangle = √[(Length)2 + (Breadth)2] Area of Semi-circle = [π × (radius)2]/2 Calculation: Area of rectangle = 2a × a = 2a2 Diagonal of rectangle = √[(2a)2 + (a)2] = √5 × a Diagonal of rectangle will be diameter of the semi-circle So radius of semi-circle = (√5 × a)/2 Area of Semi-circle = π/2 × [(√5 × a)/2]2 ⇒ Area of Semi-circle = 5a2π/8 Area of semi-circle/Area of rectangle = (5a2π/8)/2a2 ⇒ Area of semi-circle/Area of rectangle = (5 × 22 × a2)/(2 × 8 × 7 × a2) = 55/56 ⇒ Area of semi-circle/Area of rectangle = 55/56 ∴ The Ratio between the Area of semi-circle and the Area of rectangle is 55 : 56 |
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