The sum of the two sides of the rectangle is 16dm and they relate as 3: 5. Find the sides.

From the condition it is known that the sum of the two sides of the rectangle is 16 dm, and it is also known that the sides are related as 3: 5.

We will solve the problem using the equation. To begin with, we introduce the coefficient of similarity k and then write the lengths of the sides as 3k and 5k.

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

3k + 5k = 16;

We solve the resulting equation:

k (3 + 5) = 16;

8k = 16;

k = 16: 8;

k = 2 we found the coefficient of similarity and now it is quite easy to find the lengths of the sides of the rectangle:

The smaller 3 * 2 = 6 dm and the larger 5 * 2 = 10 dm.