The sides of a triangle are related as 3: 4: 5, the perimeter of this triangle is 48cm, which is equal to the smaller side of the triangle.

Let x denote one third of the length of the shorter side of this triangle.

Then the length of the smaller side of this triangle is 3x.

According to the condition of the problem, the lengths of the sides of this triangle are related as 3: 4: 5, therefore, the length of the middle side of this triangle will be 4x, and the length of the larger side of this triangle will be 5x.

By the condition of the problem, the perimeter of this triangle is 48 cm, therefore, we can draw up the following equation:

3x + 4x + 5x = 48.

We solve the resulting equation:

12x = 48;

x = 48/12;

x = 4 cm.

Knowing x, we find the length of the shorter side of this triangle:

3x = 3 * 4 = 12 cm.

Answer: The length of the smaller side of this triangle is 12 cm.