The perimeter of the ABC triangle is 64 cm. The AB side is 7 cm less than the AC

The perimeter of the ABC triangle is 64 cm. The AB side is 7 cm less than the AC side but 12 cm larger than the BC side. Find the length of each side of the ABC triangle.

By the condition of the problem, it is known that AC – AB = 7, AB – BC = 1 2;
Let us express AC from the first equation and BC from the second equation:
AC = 7 + AB;
BC = AB – 1 2;
It is known that the perimeter of a triangle is 6 4, therefore AB + BC + AC = 6 4;
Substitute AC and BC in the perimeter formula;
AB + AB – 1 2 + 7 + AB = 6 4;
3 * AB – 5 = 6 4;
3 * AB = 6 9;
AB = 2 3;
find the rest of the sides of the triangle;
AC = 7 + 2 3, AC = 3 0;
BC = 2 3 – 1 2, BC = 1 1.
Answer: AB = 2 3, AC = 3 0, BC = 1 1.