If an area enclosed by a circle or a square or an equilateral triangle is the same, then the maximum perimeter is possessed by:

**(A)** circle

**(B)** square

**(C)** equilateral triangle

**(D)** triangle and square have equal perimeters greater than that of circle

**Answer:** **(C)** **Explanation:** Let the area be a. Then,

Radius of the circle = (a/Pi)^0.5

Side of square = a^0.5

Side of equilateral triangle = (4a/3^0.5)^0.5

Therefore,

Perimeter of circle = 2*Pi*(a/Pi)^0.5 = 2*(Pi*a)^0.5 = 2*(3.14*a)^0.5 = 3.54a^0.5

Perimeter of square = 4a^0.5

Perimeter of equilateral triangle = 3(4a/3^0.5)^0.5 = 3(4a/1.732)^0.5 = 3(2.31a)^0.5 = 3*1.52a^0.5 = 4.56a^0.5

Therefore, perimeter of the equilateral triangle is the highest.

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