The perimeter of triangle ABC is 56cm. Side AB is 18cm and side BC is 3cm shorter than AB.

The perimeter of triangle ABC is 56cm. Side AB is 18cm and side BC is 3cm shorter than AB. Find the length of side AC.

As you know, the perimeter of a triangle is the sum of all sides, and is calculated by the following formula: P = AB + BC + AC.
From the condition of the problem we know: the perimeter P = 56 cm, AB = 18 cm, the other side BC = AB – 3 cm = 18 – 3 = 15 cm.
Substitute all the known values of the sides and perimeter of the triangle into the formula and find the third side: 56 = 18 + 15 + AC.
56 = 33 + AC.
AC = 56 – 33 = 23 cm.
Answer: The length of the third side of the triangle is 23 cm.