If areas of three circles are in ratio 4 : 9 : 25. What is the ratio of their radii?

Area of the circle of radius r is πr²

Answer: For the given ratio of areas of three circles  4 : 9 : 2, the ratio of the radii for three circles is r₁ : r₂ : r₃ = 2 : 3 : 5

Let's find the ratio of their radii

Explanation:

Let the three circle be C₁, C₂ and C₃ and r₁, r₂ and r₃ be the radii of these three circles respectively.

We know that the formula to find the area of a circle using the radius r is πr²

Now we have been given with the fact that areas of these circles are in the ratio of 4 : 9 : 25

⇒πr₁² : πr₂² : πr₃² = 4 : 9 : 25

Cancelling out the common factor π we get

⇒r₁² : r₂² : r₃² = 4 : 9 : 25

⇒r₁² : r₂² : r₃² = 2² : 3² : 5²

⇒r₁ : r₂ : r₃ = 2 : 3 : 5

Thus, If areas of three circles are in ratio 4 : 9 : 2 then the ratio of the radii is r₁ : r₂ : r₃ = 2 : 3 : 5.