What is the length of line segment G' A'? PLEASE HELP!!!!!

I believe the perimeter of the adult pinball machine is given as 172 in^2.
First, for the adult machine, we have:
GE = AM = 56 inch
EM = 35 inch
perimeter = 172 inch
Therefore:
GA = 172 - (56+56+35) = 172 - 147 = 25 inch

Now, the children version is a scaled down version of the adult version. This means that the sides of the version are proportional to their corresponding sides in the child version, therefore:
EM/E'M' = GA/G'A' = GE/G'E' = AM/A'M'
We have:
EM = 35 in
E'M' = 14 in
GA = 25 in
G'A' is the one we need to find

Substitute with the givens in the proportionality expression above to get G'A' as follows:
EM/E'M' = GA/G'A'
35/14 = 25/G'A'
35 G'A' = 25*14
G'A' = (25*14) / 35
G'A' = 10 inch

DerrickStalvey DerrickStalvey · Answer 2 · 2018-10-29T15:37:58+01:00

Answer:

if GA = x inches , them G'A' will be 2x/5.

Step-by-step explanation:

From given figure we can assume that GAME and G'A'M'E' are similar figures.

that is G'A'M'E' is a copy of GAME on smaller scale. But since figures are similar, ratio of there sides will be in proportion that is

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

⇒ G'A'/GA = 14/35

⇒ G'A'/GA = 2/5

so G'A' is dependent on value of GA. From given figure we can only say that GA will be less that EM that is 35 inches.

So if GA is assumed to be x , them G'A' will be 2x/5.

for once case if we assume GA to be 25 inches , then G'A' will be 2×25/5 = 10 inches.