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 line segment G'A'?

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 line segment G'A'?

adrynicoleb · Answer

Here's the models.

adrynicoleb · Answer

@jdoe0001

anonymous · Answer

Well, we need to set up a proportion, correct? Use two similar sides, and set up a side first.

adrynicoleb · Answer

35/14?

anonymous · Answer

Alright, now we have to set up the second proportion. What do you think it will be?

adrynicoleb · Answer

56/x?

anonymous · Answer

You could, if you wanted. I believe you could also use the perimeter  to find G' to A'

adrynicoleb · Answer

or 172/x?

anonymous · Answer

Honestly, I would find it on the big one first, it'll be less work.

adrynicoleb · Answer

ok so hold on a sec\

anonymous · Answer

Alright.

anonymous · Answer

Oh, i'm sorry! I meant find the length of  G to A

adrynicoleb · Answer

this is probably wrong because it seems kinda high but i got 430

anonymous · Answer

definitely wrong, because we are finding the value of a smaller figure.

anonymous · Answer

So, let's find G to A. That's our total perimeter minus our known values, because we are only missing one side.

adrynicoleb · Answer

ok so i would do 172 - 35?? im confused

anonymous · Answer

Sorry that I cut out there, anyways, perimeter is the sum of all the sides, correct? Well, say x = length of segment AG. 
35 + 56 + 56 + x = 172. 
Do you understand now?

adrynicoleb · Answer

yeah i think so. so i do 35 + 56 + 56, and then subtract it from 172??

anonymous · Answer

Exactly!

adrynicoleb · Answer

ok and then i get 25 right?

anonymous · Answer

Yes, now we can set up the second side of our proportion.

anonymous · Answer

Reminder, our first was $$\frac{ 35 }{14 }$$

adrynicoleb · Answer

ok so then it would be x/25? or the other way around?

anonymous · Answer

Remember, we but the adult pinball table on top, so the other way around.

anonymous · Answer

$$\frac{ 35 }{14} =  \frac{ 25 }{ x }$$

adrynicoleb · Answer

ohhh i remember now.  its 25/x because it is that way on the first side. got it. im gonna try to solve it hold on.

adrynicoleb · Answer

10??

anonymous · Answer

Yep! Solved.

adrynicoleb · Answer

YAY!! thank you SOOO much!! :D :D