The sum of the lengths of the sides AB and BC of the triangle ABC is 11 cm.

The sum of the lengths of the sides AB and BC of the triangle ABC is 11 cm. The sum of the lengths of the sides BC and CA is 7 cm, and the sum of the lengths of the sides AB and CA is 8 cm. Find the perimeter of the triangle ABC. Find the length of each side of this triangle.

By the condition of the problem, we have a system of three equations:
AB + BC = 11
BC + CA = 7
AB + CA = 8
We add three equations and get:
2AB + 2BC + 2CA = 26
AB + BC + CA = 13 (cm) – the perimeter of the ABC triangle.
Subtract the second from the first equation and get:
AB – CA = 4
AB + CA = 8
Add two equations:
2AB = 12
AB = 6 (cm);
CA = 8 – AB = 8 – 6 = 2 (cm);
BC = 7 – CA = 7 – 2 = 5 (cm).
Let’s check:
P = AB + BC + CA = 6 + 5 + 2 = 13 (cm).
Answer: the perimeter of the triangle is 13 cm, the sides of the triangle are 6 cm, 5 cm, 2 cm.