# Find the lengths of the sides of the triangle if their ratio is 5: 3: 4 and the perimeter of the triangle is 2.4 dm.

We denote by x one fifth of the length of the longest side of this triangle, expressed in decimeters.

Then the length of the longest side of this triangle will be 5x dm.

According to the condition of the problem, the lengths of the sides of a triangle are 5: 3: 4, therefore, the lengths of the other two sides of this triangle will be equal to 3x and 4x, respectively.

By the condition of the problem, the perimeter of this triangle is 2.4 dm, therefore, we can draw up the following equation:

5x + 3x + 4x = 2.4.

We solve this equation:

12x = 2.4;

x = 2.4 / 12;

x = 0.2 dm.

Knowing x, we find the lengths of the sides of the triangle:

5x = 5 * 0.2 = 1 dm;

3x = 3 * 0.2 = 0.6 dm;

4x = 4 * 0.2 = 0.8 dm.

Answer: the lengths of the sides of the triangle are 1 dm, 0.6 dm and 0.8 dm.