We know that both figures are similar, as they are proportionate to each other. In other words, similar figures keep their shape because their angles are still congruent, but their dimensions are proportional. When dealing with similar figures, the constant “k” is used, which k is the constant of proportionality. So, k=scale factor.
To start, because the figures are proportional, we need to setup some proportions:
480/12=144/x
We do this to divide the length of the original figure by 12, and we set them equal because their quotient should remain constant or the same. Now, we use the cross product property to solve:
480•x=144•12
480x=1728
x=3.6
Therefore, substitute x back into the proportional equation:
480/12=144/3.6
40=40
So, the height is 3.6in. This means the new figure is 1/40 of the original.
