The lengths of the sides are a, ar and ar2 so the perimeter is a(1+r+r2)=28.5cm, where a=6cm and r is the common ratio for the geometric sequence.
1+r+r2=28.5/6=4.75,
r2+r=3.75,
r2+r+0.25=4,
(r+0.5)2=22,
r+0.5=2, r=1.5. The side lengths are 6cm, 9cm, 13.5cm.