The sides of the triangle are in the ratio 3: 5: 6. The perimeter of a similar triangle is 56 dm. Find the sides of the second triangle.

From the condition we know that the sides of a triangle are related as 3: 5: 6. In order for the sides of a similar triangle, if its perimeter is 56 dm, we compose and solve a linear equation with one variable.

Let’s introduce the coefficient of similarity x, then the sides of the triangle can be written as 3x; 5x and 6x.

The perimeter of a triangle is equal to the sum of the lengths of the sides of this triangle.

3x + 5x + 6x = 56;

We solve the resulting equation:

14x = 56;

x = 56: 14;

x = 4.

We are looking for the sides of the triangle:

3x = 3 * 4 = 12 dm;

5x = 5 * 4 = 20 dm;

6x = 6 * 4 = 24 dm.

Answer: 12 dm; 20 dm; 24 dm.