The perimeter of the triangle is 86 cm, the sum of the lengths of the two sides is 62 cm.

The perimeter of the triangle is 86 cm, the sum of the lengths of the two sides is 62 cm. What will be the length of each side if the length of the third side is 13 cm shorter than the length of the first side.

Let us denote the lengths of the sides of this triangle by x1, x2 and x3.
According to the condition of the problem, the perimeter of this triangle is 86 cm, therefore, the following relationship takes place:
x1 + x2 + x3 = 86.
It is also known that the sum of the lengths of the two sides is 62 cm, therefore, the following relationship holds:
x1 + x2 = 62.
Substituting this value for x1 + x2 into the ratio x1 + x2 + x3 = 86, we get:
62 + x3 = 86;
x3 = 86 – 62;
x3 = 24 cm.
Also, according to the condition of the problem, the length of the third side is 13 cm shorter than the length of the first side, therefore, than the first side is 13 cm longer than the third side and the length of the first side is:
x1 = x3 + 13 = 24 + 13 = 37 cm.
Knowing x1, we find x2:
x2 = 62 – x1 = 62 – 37 = 25 cm.

Answer: the sides of the triangle are 37 cm, 25 cm and 24 cm.