Question

VERY EASY,MEDAL+FAN. SOMEONE PLEASE HELP
The diagram shows a section of a bridge between the points A and K. The length of line segment is AK 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = 2FK. The first pillar,BG, is 20 meters tall.

The area of ∆CDF is _____square meters.

Answer 1

http://assets.openstudy.com/updates/attachments/56c21bdce4b059857047417b-haleyshabba-1455561734914-1ede0da051bd4a47b13ca7013501ae97.jpg

Answer 2

To find the area, you need values of "CF" and "DH" from "2AC = CF = 2FK" and the fact that AK = AC+CF+FK ... we should be able to get CF...

Also, as the triangles are similar that should help in getting DH given BG is 20m...

Answer 3

so how would we find DH? I thought it would be maybe 40, just a wild guess, i dont know

Answer 4

Scale factor.

Answer 5

40/640?

Answer 6

What's 40/640?

Answer 7

or 640/40 = 16

Answer 8

The scale factor is just the length of a side on triangle divided by the length of one side of the other similar triangle.

Answer 9

how would i use 16 or scale factor in order to get my answer?

Answer 10

To know how much bigger the center triangle is.

Answer 11

DH = 16?

Answer 12

How bug is BG?

Answer 13

20

Answer 14

Right. How much bigger are the sides of the central triangle than the smaller triangles?

Answer 15

by 2? Im not sure really, cause 2AC=CF so wouldnt it be 2 times as large

Answer 16

You're right. CF=2AC "It's two times AC".

Answer 17

40 then

Answer 18

Yep.

Answer 19

so DH = 40 right?

Answer 20

Yes.

Answer 21

Now, you need to get CF.

Answer 22

600?

Answer 23

what the base?

Answer 24

Use this 2AC = CF = 2FK

Answer 25

...

Answer 26

Just make all the lengths x.
CF=2x and so on

Answer 27

40x would come out as a result,so 40 x 2= 80

Answer 28

1600