Find the ratios of the perimeters and areas of the pairs of two regular pentagons with corresponding sides that measure 48cm and 54 cm.

Answer 1

Since perimeter is a linear relationship, the ratio of perimeters of two similar figures is proportional to the ratio of their sides, thus
48 : 54 or 8 : 9

Since area is a quadratic relationship , .....
the square of their sides, thus
48^2 : 54^2 = 2304 : 2916
= 64 : 81