it's easy to work out the length of another shape through a ratio.
if the ratio is 1:2 and your smaller length is 3 than your larger length will be 6.
1. ratio - 1:3, smaller side = 4
2. ratio - 1:2.5, larger side = 6
3. ratio - 1.5, smaller side = 7
the ratio changes a little if you need to work out the area from the same two shapes.
you need to square your ratio so 1:2 = 1:4 and 1:3 = 1:9
this is because the ratio we previsouly had was to work our the lengths but area has a unit of cm^2 therefore we need to square or alernatively square root the ratio to find the area.
here the ratio changes again.
if you need to work out the volume from 2 shapes then you need to cube your ratio (the length ratio) so 1:2 = 1:8 and 1:3 = 1:27.
however if you need to work out the volume from an area ratio then you need to square root this ratio and then cube it to get the correct one.
this is because the units for volume are cm^3
to sum up...
length ratio - comes as it is, just need to work it out using the different lengths on the shapes you are given
area ratio - square the length ratio, or if you already have the area ratio and you need the length ratio then square root it
volume ratio - cube the length ratio, or if you already have the volume ratio and you need to work out the length ratio then cube root it to find the length, or if you already have the area ratio and you need to find the volume ratio then you square root the ratio and and then cube it