Given a rectangle: the sum of its two sides is 16 dm and they relate as 3: 7.

In order to find the lengths of the sides of a rectangle, if it is known that the sum of its two sides is 16 dm and they are related as 3: 7.

Let’s start by defining the coefficient of similarity as k.

Then the lengths of the sides of the rectangle can be written as 3k and 7k.

Knowing the sum of the sides of the rectangle, we can write the equation:

3k + 7k = 16;

We solve the equation:

k (3 + 7) = 16;

10k = 16;

k = 16:10;

k = 1.6 coefficient of similarity.

Let’s calculate the lengths of the sides of the rectangle:

3 * 1.6 = 4.8 dm and 7 * 1.6 = 11.2 dm.