Diagram shows a section of a bridge between the points A and K. The length of line segment is 640 meters. ∆ABC, ∆CDF, and ∆FJK a

Question

mamaluj [8]

2 years ago

10

Diagram shows a section of a bridge between the points A and K. The length of line segment is 640 meters. ∆ABC, ∆CDF, and ∆FJK a

re similar, and 2AC = CF = 2FK. The first pillar, , is 20 meters tall.
The area of ∆CDF is square meters.

Mathematics

1 answer:

Marta_Voda [28] · Answer 1 · 2022-09-09T11:51:50+03:00

AK = 640
Δ ABC and ΔFJK are similar. They are small triangles.
ΔCDF is the big triangle.

640 / 2 = 320 m= CF
AC & FK= 320/2 = 160 m each

2AC = CF = 2FK
2(160) = 320 = 2(160)

BG = 20 m

20/160 = x / 320
20*320 = 160x
6400 = 160x
6400/160 = x
40 = x

Area of CDF = (40 m * 320 m)/2 = 12,800 / 2= 6,400 m²