Answer
$ \dfrac{5}{2}$
and $5: 2$
Work Step by Step
We can see that the ratio of the perimeters of two smaller figures is $\dfrac{a}{b}$, and the ratio of their areas is the square of the ratio of their perimeters:
$\dfrac{a^2}{b^2}$.
Set up a proportion:
$\dfrac{a^2}{b^2}=\dfrac{75}{12} \\ \dfrac{a}{b}=\sqrt {\dfrac{25}{4}}$
This implies that the square factor is $ \dfrac{a}{b}=\dfrac{5}{2}$
So, the ratio of the perimeters is equal to the scale factor, which is $5: 2$
