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: Adult pinball machine GAME with base ME measuring 35 inches and sides measuring 56 inches. Child pinball machine G prime A prime M prime E prime with base M prime E prime measuring 14 inches

If the perimeter of the adult pinball machine is 167 inches, what is the length, in inches of Segment line G prime A prime?

Answer 1

Answer: 8 inches

Step-by-step explanation:

Here, GAME and G'A'M'E' are two quadrilaterals,

In which, EM = 35 inches, GE=AM = 56 inches, E'M' = 14 inches,

And, Perimeter of GAME = 167 square inches.

⇒ AG = 167 - ( GE + EM + MA) = 167 - (56+35+56) = 167 - 147 = 20 inches

According to the question,

Quadrilaterals GAME and G'A'M'E' are similar,

⇒ $\frac{AG}{EM} = \frac{G'A'}{E'M'}$

⇒ $\frac{20}{35} = \frac{G'A'}{14}$

⇒  $G'A' = 14\times \frac{20}{35}$

⇒ $G'A' = \frac{280}{35}$

⇒ $G'A' = 8$

Thus, the length of line segment G'A' = 8 inches.

Answer 2

First, you need to add all sides of the adult pinball machine which will give you 147. Then, in order to find the length of GA, you need to subtract the perimeter which is 167, by 147 which will give you 20. GA = 20

Now in order to find G'A', you need to cross multiply 14/35 = G'A'/20

You should end up with 280 = 35. Divide 35 by 280 and you get 8.

The correct answer is 8