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? Type the numeric answer only in the box below.

Answer 1

The correct answer is 8

Answer 2

8 inches

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,

`(ME)/(M'E')=(GA)/(G'A')`

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

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