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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? Type the numeric answer only in the box below.

Verified Answer :

taniyahavenger

The correct answer is 8

Answer:

8 inches

Step-by-step explanation:

Given,

In two quadrilateral GAME and G'A'M'E',

ME = 35 inches, AM = GE = 56 inches,

M'E' = 14 inches,

Also, the perimeter of quadrilateral GAME = 167 inches,

⇒ GA + AM + ME + GE = 167

⇒ GA + 56 + 35 + 56 = 167

⇒ GA + 147 = 167

⇒ GA = 20 inches.

Now, GAME is similar to G'A'M'E' are similar,

By the property of similar figures,

\(\frac{ME}{M'E'}=\frac{GA}{G'A'}\)

\(\implies G'A'=\frac{M'E'\times GA}{ME}=\frac{14\times 20}{35}=\frac{280}{35}=8\text{ in}\)

Hence, the length of Segment line G'A' is 8 inches.

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