In triangle ABC AB + BC = 25cm, BC + AC = 26cm, AC + AB = 27cm.Find the perimeter of triangle ABC and each side.

Let us express the AB side.
AB = 25 – BC
Substitute this expression into the sum of AC and AB by the condition:
AC + AB = 27
AC + (25 – BC) = 27
AC – BC = 27 – 25 = 2
AC = BC + 2
Substitute the resulting expression into the sum of BC and AC:
BC + (BC + 2) = 26
2 * BC + 2 = 26
2 * BC = 24
BC = 24: 2
BC = 12 cm.
Let’s find the AC:
AC = 12 + 2 = 14 cm.
Find AB:
AB + 12 = 25
AB = 25 – 12 = 13 cm.
Find the perimeter:
AB + BC + AC = 13 + 12 + 14 = 39 cm.
Answer: BC = 12 centimeters, AC = 14 centimeters, AB = 13 centimeters, the perimeter of the ABC triangle is 39 centimeters.