Question

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

Answer 1

Area of ΔCDF = 6400 m²

Step-by-step explanation:

Here,

AK = 640 m

ΔABC and ΔFJK are similar. They are small triangles.

ΔCDF is the big triangle

640/2  = 320 m = CF

AC and 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 = 160 x

x = 6400/160

x = 40

Area of ΔCDF = (40 * 320)/2

                        = 12,800/2

                         = 6400 m²