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in Perimeter and Area of Plane Figures by (23.5k points)
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The area of a square and circle is same and the perimeter of square and equilateral triangle is same, then the ratio between the area of circle and area of equilateral triangle is:

(a) π : 3 

(b) 9 : 4√3 

(c) 4 : 9√3 

(d) None of these

1 Answer

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Best 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 = \(\frac{4a}{3}\).  

∴ Area of equilateral triangle = \(\frac{\sqrt3}{4}b^2\) = \(\frac{\sqrt3}{4}\)\(\bigg(\frac{4a}{3}\bigg)^2\) 

\(\frac{\sqrt3}{4}\) x \(\frac{16a}{9}\) = \(\frac{4\sqrt3a^2}{9}\)

∴ Required ratio between area of circle and area of equilateral Δ is a2\(\frac{4\sqrt3a^2}{9}\) = 9 : 4√3.

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