If an area enclosed by a circle or a square or an equilateral triangle is the same then the maximum ...........

Quantitative Aptitude ( CCS) Mensuration 2D

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

circle

square

equilateral triangle

triangle and square have equal perimeters greater than that of circle

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Explanation:

Let the area be a. Then,
Radius of the circle = (a/π )^0.5
Side of square = a^0.5
Side of equilateral triangle = (4a/3^0.5)^0.5
Therefore,
Perimeter of circle = 2*π *(a/π)^0.5= 2*(π*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.