The ratio of the perimeters of such triangles is 3/5. What is the ratio of their areas?

1. According to the properties of such triangles, their sides opposite equal and angles are proportional. Therefore, the total length of the sides of one triangle (perimeter) and the sum of the lengths of the sides (perimeter) of another triangle similar to it are also proportional. Their ratio is equal to the value of the k-coefficient of similarity.

2. By the statement of the problem, the ratio of the perimeters of the triangles is 3/5. That is, k = 3/5.

3. According to the properties of similar geometric figures in the form of triangles, the ratio of their areas is equal to k².

4.k² = (3/5) ² = 9/25.

Answer: the quotient from dividing the area of ​​one triangle to the area of ​​another triangle similar to it is 9/25.