the areas of two similar plain figures are in the ratio 36 : 25 what is the ratio of their sides? what is the ratio of their perimeters?

Similar figures are similar in all respects.

The ratio of the lateral sides and perimeters = the ratio of square root of their areas

Then, the ratio of the sides and the perimeters is 6:5

If areas are in the ratio  a² / b²,  their corresponding lengths will be in the ratio  a / b.

Since the area are in the ratio  36 / 25,  their corresponding lengths will be in the ration  6 / 5.

The ratio of their sides will be 6 : 5.

Since perimeters are lengths, the ratio of their perimeters is also  6 : 5.

To explain why:

If the areas are 36 and 25, they could both be squares; a square with an area of 36 has a side length of 6; a square with an area of 25 has a side length of 5; thus, the ratio of sides is 6:5.

The perimeters of the above squares are 24 and 20; a ratio of 24:20, which reduces to 6:5.