QA – Placement Quizzes | Mensuration 2D | Question 11
If an area enclosed by a circle or a square or an equilateral triangle is the same, then the maximum perimeter is possessed by:
(C) equilateral triangle
(D) triangle and square have equal perimeters greater than that of circle
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
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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