The areas of two similar polygons are in the ratio 36:81 find the ratio of the corresponding sides

Answer 1

If you think of these as two squares, one larger than the other, then side²=36 tells you one side. side²=81 tells you another side. Take a ratio of these.

If you think of these as isosceles right triangles, one larger than the other, then (1/2)*side²=36 for one triangle, and (1/2)*side²=81 for the other. If you take the ratio of these two sides it should agree with the answer for the square. I suspect this works for all polygons.