PLEASE PLEASE HELP!! 13. (04.01 MC)
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.
60 ft
3 in
4 in
D
2 in
B
0 2 in
G
What is the total length, in feet, of the actual walkway? (5 points)

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