In triangle ABC, side AB is 1 cm larger than side BC and 1 cm less than side AC.

In triangle ABC, side AB is 1 cm larger than side BC and 1 cm less than side AC. Find the perimeter of triangle ABC if it is known that AC = 6 cm.

After reading the condition of the problem, we will immediately denote AB as x for convenience, then BC will be equal to (x – 1), and AC will be equal to (x + 1), but by the condition we know the value of AC, from here we will find the value of AB at once:
x + 1 = 6,
x = 5 centimeters, we got that AB is 5 cm, then BC is 4 cm, all sides are known, we can find the perimeter by adding all the lengths:
4 + 5 + 6 = 15 cm.
Answer: 15 centimeters.