What is the circumference of a circle whose area is equal to that of an equilateral triangle with perimeter P?
Explanation:
Perimeter of the equilateral triangle = P
∴ Side of the equilateral triangle = P/3
∴ The area of the equilateral triangle = 34×P32
But the area of the equilateral triangle is equal to the area of the circle.
Area of the circle = πr2 = 34×P32
∴ Radius of the circle, r = 3π×P6
∴ The circumference of the circle = 2πr = (π3)3P
Hence, option (d).
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