Quadrilateral abcd in the figure below represents a scaled-down model of a walkway around a historic site. quadrilateral efgh represents the actual walkway. abcd is similar to efgh. what is the total length, in feet of the actual walkway?

Step-by-step explanation:

If the figure A and the figure B are similar in scale k, then the ratio corresponding sides is equal k, and the ratio of perimeter is equal to k.

Calculate the scale:

Lets P₂ - the perimeter of the quadrilateral EFGH.

Calculate the perimeter of the quadrilateral ABCD:

P₁ = 3 + 3 + 6 + 4 = 16 in.

Substitute to:

     multiply both sides ny 16

Convert to the feet:

  108 ft

Step-by-step explanation:

The total length in inches of the perimeter of the model is ...

  7 in + 3 in + 3 in + 5 in = 18 in

The total length of the walkway will have the same ratio to this perimeter that the corresponding sides have:

  EF/AB = 42 ft/(7 in) = (walkway length)/(18 in)

Multiplying by 18 in, we get ...

  walkway length = (42 ft)(18 in)/(7 in)

  walkway length = 108 ft

108 feet²

Step-by-step explanation:

Well we can just multiply the corresponding sides of Quadrilateral ABCD to fit Quadrilateral EFGH.

Line EF is 42 feet

Line FG is 18 feet

Line GH is 18 feet

Line HE is 30 feet

The perimeter of Quadrilateral EFGH is

30+18+18+42=

30+36+42=

66+42=

108 feet²

165 ft

Step-by-step Explanation:

==>Given:

Quadrilateral ABCD (scaled-down model of walkway) ~ Quadrilateral EFGH (walkway)

EF = 60ft

AB = 4 in

BC = 2 in

CD = 2 in

DA = 3 in

==>Required:

Total length (Perimeter) of actual walkway.

==>Solution:

Since ABCD ~ EFGH, the ratio of their corresponding sides would be the same.

Thus, it means, EF/AB = FG/BC = GH/CD = HE/DA

Since, we know the length of one side of Quadrilateral EFGH, we can find the scale factor, which we would use in solving for the perimeter of Quadrilateral EFGH.

EF = 60 ft

AB = 4 in

EF/AB = scale factor

Note: 60 ft should be converted to inches. Both corresponding side must be in the same unit if we are to set their ratio.

1 ft = 12 in

Therefore, 60 ft = 60 × 12 = 720 in = EF

720/4 = 180

The scale factor = 180.

Calculate the total length of Quadrilateral ABCD

Perimeter/total length = AB + BC + CD + DA

= 4 + 2 + 2 + 3

= 11 inches

Find the total length of Quadrilateral EFGH by multiplying the perimeter of ABCD (11 inches) by the scale factor we got (180)

Perimeter of EFGH = 11 × 180 = 1,980 inches

Convert the total length to ft

12 in = 1 ft

1,980 in = 1,980/12 = 165 ft

Total length of of the actual walkway (EFGH) = 165 ft

165ft

Step-by-step explanation:

Ratio of actual walkway and a model is :

60  ( Ft ) : 15 ( in)  or : 15 : 1

EF = 60 Ft,

FG = 30 Ft,

GH = 30 Ft,

HE = 45 Ft.

60 + 30 + 30 + 45 = 165 Ft

192 Feet

Step-by-step explanation:

192 feet

Step-by-step explanation:

Since we know that ABCD and EFGH are similar, they are just scaled differently, we know the ratio between each corresponding segment will be the same.

If we take corresponding segments AB and EF, we know that AB is 6 inches, and that EF is 72 feet, so the ratio is 144 (72/6 = 12, then 12 inches per foot).  To make it simple, let's say 12... and we change the unit from ft to inches. Meaning EF is 12 times longer (in feet) than AB is (in inches).

So, the lengths of the actual pathway are:

EF = 72 ft

FG = 36 ft (3 * 12)

GH = 36 ft (3 * 12)

EH = 48 ft (4 * 12)

So, the total length of the pathway is: 72 + 36 + 36 + 48 = 192 feet

The answer is 165. I just took the test and got it correct

the picture in the attached figure

Step 1

Find the perimeter of the scaled-down model of a walkway (Quadrilateral ABCD)

Step 2

Find the scale factor

if Quadrilateral ABCD is similar to Quadrilateral EFGH

then

Step 3

Find the perimeter of the actual walkway (Quadrilateral EFGH)

therefore

the answer is