If the areas of two similar triangles are in the ratio 196 : 625,what would be the ratio of the corresponding sides?

Solution

ATQ, The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths. Let the ratio of the corresponding side lengths be a:b. Then, the ratio of their areas would be (a²) : (b²). Given that the ratio of the areas is 196:625, we can set up the equation: (a²) : (b²) = 196 : 625 To find the ratio of the corresponding side lengths, we can take the square root of both sides of the equation: √[(a²) : (b²)] = √(196 : 625) Simplifying, (a/b) = √(196/625) (a/b) = 14/25 Therefore, the ratio of the corresponding side lengths is 14:25.