Question 917723
{{{s}}}= side length for the smaller square
{{{S}}}= side length for the larger square
{{{s/S=2/3}}}
 
1) {{{4s}}}= perimeter for the smaller square
{{{4S}}}= perimeter for the larger square
The ratio of the perimeters is
{{{4s/4S=(4/4)(s/S)=1*(2/3)=2/3}}}
 
2) {{{s^2}}}= area for the smaller square
{{{S^2}}}= area for the larger square
The ratio of the areas is
{{{s^2/S^2=(s/S)^2=(2/3)^2=2^2/3^2=4/9}}}
 
NOTE: For similar shapes (two squares, two cubes, two circles, two spheres, etc),
all measures of length (side, perimeter, radius, diameter, circumference, etc) are in the same ratio.
If that ratio is {{{r}}} ,
The ratio of corresponding areas is {{{r^2}}} ,
and the ratio of corresponding volumes is {{{r^3}}} .
That works for any kind of shape, as long as one is a scaled up or scaled down version of the other.