The sides of the triangle are 7: 6: 3. Find the sides of a similar triangle if its perimeter is 8 cm.

Let a denote one third of the length of the shorter of the sides of such a triangle.

Then the length of this smaller side should be 3 cm.

Since a similar triangle has a ratio of the lengths of the sides is seven to six to three, then the ratio of the lengths of the sides will be the same for the desired triangle.

Therefore, the lengths of the other two sides should be 6a cm and 7a cm.

Since the perimeter of the desired triangle is 8 cm, we can make the following equation:

3a + 6a + 7a = 8,

solving which, we get:

16a = 8;

a = 8/16 = 0.5 cm.

We find the lengths of all sides:

3a = 3 * 0.5 = 1.5 cm;

6a = 6 * 0.5 = 3 cm;

7a = 7 * 0.5 = 3.5 cm.

Answer: 1.5 cm, 3 cm and 3.5 cm.