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      Question

      The area of an equilateral triangle is 432√3

      cm2 . If a square is drawn using the height of the triangle as one of the sides, then find the difference between the perimeter of the square and the triangle. 
      A 72(5 - √3) cm Correct Answer Incorrect Answer
      B 72(2 - √3) cm Correct Answer Incorrect Answer
      C 52(3 - √2) cm Correct Answer Incorrect Answer
      D 77(2 - √3) cm Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ, Area of equilateral triangle = (√3/4) X side2 Let the side of the given triangle be 'a' cm. ATQ; 432√3 = (√3/4) X a2 Or, 432 X 4 = a2 So, 'a' = ± 24√3 Since, side cannot be negative, a = +24√3 Height of equilateral triangle = (√3/2) X side So, height of the given triangle = (√3/2) X 24√3 = 36 cm So, length of each side of the square = 36 cm So, perimeter of the square = 36 X 4 = 144 cm And perimeter of the triangle = 24√3 X 3 = 72√3 cm So, required difference = 144 - 72√3 = 72(2 - √3) cm

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