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.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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