The area of a square and circle is same and the perimeter of square and equilateral triangle is same, -Maths 9th

The area of a square and circle is same and the perimeter of square and equilateral triangle is same, -Maths 9th
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1 Answer

Answer :

(b) 9 : 4√3.Let each side of the square = a cm. Then, Area of square = a2 cm2 Also, let r be the radius of the circle. Then, πr2 = a2 Let each side of the equilateral triangle = b cm. Then 3b = 4a ⇒ b = \(rac{4a}{3}\).  ∴ Area of equilateral triangle = \(rac{\sqrt3}{4}b^2\) = \(rac{\sqrt3}{4}\)x \(\bigg(rac{4a}{3}\bigg)^2\) = \(rac{\sqrt3}{4}\) x \(rac{16a}{9}\) = \(rac{4\sqrt3a^2}{9}\)∴ Required ratio between area of circle and area of equilateral Δ is a2 : \(rac{4\sqrt3a^2}{9}\) = 9 : 4√3.
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