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    Question

    The area of an equilateral triangle is given as 432

    √3 cm2 . A square is constructed such that one of its sides is equal to the height of the triangle. Calculate the difference between the perimeters of the square and the triangle.
    A 36(2 - √3) cm Correct Answer Incorrect Answer
    B 36(√3 - 2) cm Correct Answer Incorrect Answer
    C 144(2 - √3) cm Correct Answer Incorrect Answer
    D 72(√3 - 2) cm Correct Answer Incorrect Answer
    E 72(2 - √3) cm Correct Answer Incorrect Answer

    Solution

    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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