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:
If the perimeter of the adult pinball machine is 172 inches, what is the length, in inches of Segment line G prime A prime?

Answer 1

First we need to find the distance from G to A, or the length of segment GA

For now we'll call this x since it's unknown. This value x adds to the other three sides of the figure to get the perimeter to be 172 inches (given)

So,

EG + GA + AM + ME = perimeter

56 + x + 56 + 35 = 172

x+147 = 172

x+147-147 = 172-147 .... subtract 147 from both sides

x = 25

So segment GA is 25 inches

We'll use this to find the length of segment G'A' which corresponds to GA

The other horizontal sides EM and E'M' also correspond, so we'll pair these sides up and form the proportion below

(GA)/(G'A') = (EM)/(E'M')

which turns into this

25/y = 35/14

when we use y in place of G'A'. Like x, y is unknown at first until we solve for it. Let's isolate y

25/y = 35/14

25*14 = y*35 .... cross multiply

350 = 35y

35y = 350

35y/35 = 350/35 .... divide both sides by 35

y = 10

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Final Answer: The length of G'A' is 10 inches