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      Question

      What is the area of the circular Track?

      Statement-I: The area of equilateral triangle that can be inscribed in circular Track is 48√3 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 β€œI and II” 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 theΒ 
      A A Correct Answer Incorrect Answer
      B B Correct Answer Incorrect Answer
      C C Correct Answer Incorrect Answer
      D D Correct Answer Incorrect Answer
      E E Correct Answer Incorrect Answer

      Solution

      Statement I:Area of equilateral triangle = 48√3 m2. (√3/4) Γ— (side) 2 = 48√3 Side = √192 = 8√3 m Statement I: Area of equilateral triangle = 48√3 m2. (√3/4) Γ— (side) 2 = 48√3 Side = √192 = 8√3 m Therefore, AD = √[(8√3)Β² – (4√3)Β²] = √144 = 12 m So, radius of circular field = OA = (2/3) Γ— 12 = 8 m Therefore, area of the circular garden = Ο€T 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 =√196 = 14 m So, diagonal of square = √2 Γ— side of square = 14√2 m Also, diagonal of square = diameter of circular garden So, radius of circular garden = 14√2/2 = 7√2 m Therefore, area of circular garden = Ο€ (7√2)Β² = 308 mΒ² Therefore, questions can be solved using statement-ll alone. Hence, option c.

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