Rectangles rectangles

Rectangle ABCD is similar to rectangle WXYZ with sides in a ratio of 4:1. What is the ratio of the areas of the two rectangles? Say a rectangle has the dimensions of 1x1 its area is 1 say the other rectangle has dimensions of 4x4 its area would be 16. 16 is 16 times bigger then 1(duh) i'm not to good at explaining but i will try.

all rectangles are 2 dimensional shapes

a way to make ratios a little easier is to but the ratios to X

like so 4X:1X

which means that there are 2 sides that 4 times bigger then X

and there are 2 sides that are 1 times bigger then X 

so both numbers become squared like so

(4^2)X:(1^2)X

4 squared is 16

1 squared is still 1

so the new ratio is

16X:1X

meaning the areas are always 16 times larger

Suppose the dimensions of each rectangle are tripled

doing this will cause and increase of area in both rectangles

but the rectangles' areas will still be within the ratio

like so

16X*3:1X*3

equals

48X:3X

48 is still 16 times large then 3