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 $π=\frac{22}{7}$)
Answer & explanation
Correct answer: option 4
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