I think you meant to say the ratio of the areas (not perimeters). Also, HKO and FGO are not showing up, so it seems like a different problem. I'm going to answer the question you posted in the image attachments.
The triangle ABC has area 12 since
A = b*h/2 = 4*6/2 = 24/2 = 12
Triangle CEF has area 48 because
A = b*h/2 = 8*12/2 = 96/2 = 48
The ratio of the areas is found by dividing the area of ABC over the area of CEF (as the last box instructs) so we have 12/48 = 1/4
Therefore, the area of ABC is 1/4 that of the area of CEF
----------------------
In summary,
Answer for the first box: 12
Answer for the second box: 48
Answer for the third box: 1/4