the complete question in the attached figure
if the tiles are similar
then
the ratio r= PQ/NM=(5.8/4.64)=1.25
let
P1 ------------- > perimeter of the smaller tile
P2------------- > perimeter of the larger tile
P2= 23 cm
P2=r*P1---------- > P1=P2/r=23/1.25=18.4 cm
the answer is 18.4 cm