Question

the ratio of the areas of two similar palygons is 121/64. what is the ratio of the perimeters

Answer 1

If you scale a certain figure with a scale factor of $k$, the sides will vary linearly, while areas will scale quadratically.

So, for example, if $k=5$, the perimeter will be 5 times as much, while the area will be 25 times as much.

So, in your case, if the area scaled by 121/64, the perimeter scaled by

$\sqrt{\dfrac{121}{64}}=\dfrac{11}{8}$