Notice that the fact that they tell us they're decagons 
has nothing at all to do with the problem.  They could be
triangles, circles, trapezoids, parallelograms, or any
shape.

If you are given:

two similar plane figures,
two corresponding areas on their surfaces, measuring A1 and A2
two corresponding lengths on their surfaces, measuring L1 and L2,

then



So A1 = 625 and A2 = 100. Plugging in:





Reduce the fraction on the right:



Take positive square roots of both sides:



 

So the ratio of perimeters is 5 to 2.

Edwin