The area of a circular park is very nearly equal to seven-fifteenth of the area of a triangular field having sides 110 m. 600 m and 610 m. What is the diameter of the park? (Take $π=\frac{22}{7}$)

140 m

We know that,

Area of right angled triangle = \(\frac{1}{2}\) × Base × Height

Area of circle = πr²

We have,

The sides of the triangle are 110 m, 600 m, and 610 m.

Area of circular park = \(\frac{7}{15}\) × Area of the triangular field

Area of right angled triangle = \(\frac{1}{2}\) × 600 × 110  = 33000

Area of circular park = \(\frac{7}{15}\) × 33000 = 15400

= πr² = 15400

= \(\frac{22}{7}\) × r² = 15400

= r² = 15400 × \(\frac{7}{22}\)

= r = \(\sqrt {4900}\) = 70m

Diameter of circular park = 2 × 70 = 140 m