Given a triangle with sides 6,8 and 12, find the sides of a triangle like this one if its perimeter is 13.

From the condition we know that a triangle is given with sides 6, 8 and 12. In order to find the sides of a triangle similar to this one, if its perimeter is 13, let’s first of all find the coefficient of similarity.

For similar triangles, the coefficient of similarity can be found as the ratio of the perimeters of these triangles.

We are looking for the perimeter of the first triangle:

P = a + b + c = 6 + 8 + 12 = 26.

Let’s find the coefficient of similarity:

P2 / P1 = 13/26 = 1/2.

Find the sides of the triangle:

6 * 1/2 = 3;

8 * 1/2 = 4;

12 * 1/2 = 6.

Answer: 3; 4; 6.