Question 29

A circle, square, equilateral triangle and regular pentagon have the same areas. Arrange the following in ascending order based on their perimeters.
(A) Circle
(B) Square
(C) Equilateral triangle
(D) Regular pentagon

Solution

A circle is the most efficient shape — it covers the most area for a given perimeter, or needs the least perimeter for a given area.

As a regular polygon gets more sides, it starts to resemble a circle, and its perimeter for the same area becomes smaller.

1. Equilateral Triangle (3 sides): Fewest sides, largest perimeter.

2. Square (4 sides): More sides, smaller perimeter than a triangle.

3. Regular Pentagon (5 sides): More sides, smaller perimeter than a square.

4. Circle (infinite sides): Most efficient, smallest perimeter for given area.

Therefore, the perimeters in ascending order are:

(A) Circle < (D) Regular pentagon < (B) Square < (C) Equilateral triangle.

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A circle, square, equilateral triangle and regular pentagon have the same areas. Arrange the following in ascending order based on their perimeters.(A) Circle(B) Square(C) Equilateral triangle(D) Regular pentagon