Question
What is the area of the circular Track?
Statement-I: The area of equilateral triangle that can be inscribed in circular Track is 48β3 m2 Statement-II: The area of square of maximum size that can be inscribed in a circular Track is 196 m2. The question consists of two statements numbered βI and IIβ given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A. The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question. B The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question. C The data either in statement I alone or in statement II alone are sufficient to answer the question. D The data given in both statements I and II together are not sufficient to answer the question. E The data in both statements I and II together are necessary to answer theΒSolution
Statement I:Area of equilateral triangle = 48β3 m2. (β3/4) Γ (side) 2 = 48β3 Side = β192 = 8β3 m 
Statement I: Area of equilateral triangle = 48β3 m2. (β3/4) Γ (side) 2 = 48β3 Side = β192 = 8β3 m Therefore, AD = β[(8β3)Β² β (4β3)Β²] = β144 = 12 m So, radius of circular field = OA = (2/3) Γ 12 = 8 m Therefore, area of the circular garden = ΟT Γ 8 Γ 8 = 64Ο mΒ² Therefore, the question can be solved using statement-l alone. Statement-II: Are of square = 196 mΒ² So, side of square =β196 = 14 m So, diagonal of square = β2 Γ side of square = 14β2 m Also, diagonal of square = diameter of circular garden So, radius of circular garden = 14β2/2 = 7β2 m Therefore, area of circular garden = Ο (7β2)Β² = 308 mΒ² Therefore, questions can be solved using statement-ll alone. Hence, option c.
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