Atoy 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 segment line g prime a prime?

Both pinball machine are identical.

Length of is 10 inches.

Perimeter of adult pinball machine = 172 inches

inches

∵ Both pinball machine are identical so

Therefore, Length of is 10 inches.

Fore more information:

link

First we need to find the distance from G to A, or the length of segment GA

For now we'll call this x since it's unknown. This value x adds to the other three sides of the figure to get the perimeter to be 172 inches (given)

So,

EG + GA + AM + ME = perimeter

56 + x + 56 + 35 = 172

x+147 = 172

x+147-147 = 172-147 subtract 147 from both sides

x = 25

So segment GA is 25 inches

We'll use this to find the length of segment G'A' which corresponds to GA

The other horizontal sides EM and E'M' also correspond, so we'll pair these sides up and form the proportion below

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

which turns into this

25/y = 35/14

when we use y in place of G'A'. Like x, y is unknown at first until we solve for it. Let's isolate y

25/y = 35/14

25*14 = y*35 cross multiply

350 = 35y

35y = 350

35y/35 = 350/35 divide both sides by 35

y = 10

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

good job you smart son of a gun you are smarter that einstein. 7