The areas of two similar triangles are 16 and 25. What is the ratio of a pair of corresponding sides?

4:5

To find the ratio of corresponding sides of two similar triangles, we can use the property that the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Let's assume that the ratio of the corresponding sides of the two triangles is represented by the variable "x".

The given areas of the two triangles are 16 and 25. Let's label the areas as A₁ and A₂, respectively.

According to the property mentioned above, we have the following equation:

A₁ / A₂ = (x₁ / x₂)²

Substituting the given values, we get:

16 / 25 = (x₁ / x₂)²

To solve for the ratio of the corresponding sides (x₁ / x₂), we take the square root of both sides:

√(16 / 25) = √((x₁ / x₂)²)

Simplifying further:

4 / 5 = x₁ / x₂

So, the ratio of the corresponding sides is 4 : 5.