Question

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 1

(c) 

Let the radius of the circle = r units, 

Length of each side of the square = a units 

Length of each side of the equilateral triangle = x units

Thus we can see that the perimeter of the triangle is the greatest.