7. In triangle ABC, side AB is 2 cm shorter than side

AC, while side BC is 1 cm longer than AC. If the

perimeter is 62 cm, find the lengths of the 3 sides.

AC = 21, AB = 19, and BC = 22

Step-by-step explanation:

If x is the length of AC, then:

AB = x - 2

BC = x + 1

The perimeter is the sum of all three sides:

62 = x + x - 2 + x + 1

62 = 3x - 1

63 = 3x

x = 21

Therefore:

AC = 21, AB = 19, and BC = 22