We are given that the perimeter of two circles is in the ratio 2:3. We need to find the ratio of their areas.


The perimeter of a circle is the distance around its outer edge. It is also known as the circumference of the circle. The formula to calculate the perimeter of a circle is given by:

P = 2πr

Where P is the perimeter, and r is the radius of the circle.


Let's assume the perimeters of the two circles are 2x and 3x respectively. We can write the ratio as:

Perimeter of Circle 1 : Perimeter of Circle 2 = 2x : 3x


The radius of a circle is half the diameter. Since the circumference of a circle is directly proportional to its radius, the ratio of the radii will be the same as the ratio of the perimeters.

Radius of Circle 1 : Radius of Circle 2 = 2x : 3x


The formula to calculate the area of a circle is given by:

A = πr^2

Where A is the area, and r is the radius of the circle.

The ratio of the areas of the two circles will be the square of the ratio of their radii:

Area of Circle 1 : Area of Circle 2 = (2x)^2 : (3x)^2

Simplifying the above expression, we get:

Area of Circle 1 : Area of Circle 2 = 4x^2 : 9x^2

Area of Circle 1 : Area of Circle 2 = 4 : 9


The ratio of the areas of the two circles is 4:9.