The area of a circular park is 37 times the area of a triangular field with sides 20 m, 20 m and 24 m. What is the perimeter (nearest to an integer) of the circular park?

The given triangular field is isosceles with two equal sides = 20 m and third side = 24 m

=> Height of triangle = $$\sqrt{(20)^2-(12)^2}=\sqrt{400-144}$$

= $$\sqrt{256}=16$$ m

Let radius of circular field = $$r$$ m

Thus, area of circular field = $$\pi r^2=37\times\frac{1}{2}\times24\times16$$

=> $$r^2=\frac{7}{22}\times37\times24\times8=\frac{49728}{22}$$

=> $$r=\sqrt{2260}\approx47.5$$ m

$$\therefore$$ Perimeter of circular park = $$2 \pi r$$

= $$2\times3.14\times47.5\approx300$$ m

=> Ans - (A)