The length of line segment AK is 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = 2FK. The first pillar is 20 meters tall. What is the area of ∆CDF

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Mathematics

Ashtyn Pace

14 May, 07:18

The length of line segment AK is 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = 2FK. The first pillar is 20 meters tall. What is the area of ∆CDF

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Fawn · Answer 1

A to K = 640 meters

2AC = CF = 2FK

2AC = 2 (160) = 320

CF = 320

2FK = 2 (160) = 320

AC = 160

CF = 320

FK = 160

AK 640

BG = 20 m; Area = (160m*20m) / 2 = 3,200/2 = 1,600 m²

20:160 = x : 320

20*320 = 160x

6,400 = 160x

6,400/160 = x

40 = x

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