Question

A toy company manufactures arcade games. They are marketing a new pinball machine to children. It is similar in size to the adult version of the same game. Both the adult and child models are shown below

Answer 1

If the perimeter of the adult pinball machine is 167 inches, what is the length, in inches ofG'A' ? Type the numeric answer only in the box below. (4 points)

Answer 2

If you have any two similar figures, then the lengths of the second figure are always a fixed scale factor difference to the original. In other words, matching sides of similar figures are in proportion.

In general:


\[\frac{ a }{ A } = \frac{ b }{ B } =\frac{ c }{ C } = \frac{ d }{ D }\]

So in order to find G'A', you are required to know what GA is (use the perimeter of the large figure to help you find GA).
Then you calculate the scale factor using a pair of matching sides from both figures (E'M' and EM)

This tells you that all the lengths of the child machine is \[\frac{ E'M' }{ EM } = \frac{ 14 }{ 35 } = \frac{2}{5}\]
times that of the corresponding lengths in the adult version.
So G'A' must also be 2/5 times that of its corresponding side GA since the scale factor is the same for corresponding sides in similar figures.
\[\frac{ E'M' }{ EM } = \frac{ G'A' }{ GA }\ = 2/5]