The perimeter of this isosceles triangle is 22 cm. if one side is 6 cm, what are the possible lengths of the other two sides? part b explain how you know. provide at least one reason for your answer.

We know that

the isosceles triangle has two equal sides

let's analyze two cases

first case
perimeter=22 cm
let's suppose that the known side of 6 cm is one of the two equal sides
perimeter=6+6+x
22=6+6+x> x=22-12> x=10 cm

answer first case
the possible lengths of the other two sides are
6 cm 
10 cm

second case
let's suppose that the known side of 6 cm is the side that is not equal
perimeter=22 cm
perimeter=6+x+x
22=6+x+x> 2x=22-6> 2x=16> x=8 cm

answer second case
the possible lengths of the other two sides are
8 cm 
8 cm