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.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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