Question 403088
The IMPORTANT key is to realize that "the ratio 5:2:4" in this problem can be translated to mean

"5 'parts', 2 'parts', 4 'parts'"

the longest side is 15cm, so that means that 15cm = 5 'parts'

so 1 'part' = 3cm

the shortest side is 2 'parts' 

the perimeter is the sum of all sides = total of 11 parts 

so,

the shortest side is 6cm
the perimeter is 33cm