Difficult# Ratios in Similar Triangles

ACTMAT-6XVFYW

In the figure below:

$$ {\Delta}CDE \sim {\Delta}BDF \sim {\Delta}ADG $$

...the ratio of the area of $ {\Delta}ADG $ to the area of $ {\Delta}CDE $ is $49 : 4$, and the ratio of the perimeter of $ {\Delta}BDF $ to the perimeter of $ {\Delta}CDE $ is $5 : 2.$

What is the ratio of the length of $ {\overline{AB}} $ to the length of $ {\overline{BC}} $?