△GHI is similar to △KLM. If the ratio of Perimeter of △GHI:Perimeter of △KLM=9:4 and the length of GH is 27cm, what is the length of the corresponding side KL?

For similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides:
Perimeter of △KLM
Perimeter of △GHI
​
=
KL
GH
​

Given that the ratio of perimeters is 9:4 and GH=27cm:

4
9
​
=
KL
27
​

9×KL=27×4
KL=
9
27×4
​

KL=3×4=12cm