Points B, D, and Fare midpoints of the sides of angle ACE. EC = 39 and DF = 18. Find AC

Mathematics

1 answer:

Dmitry [639]3 years ago

6 0

Answer: Line AC = 36

Step-by-step explanation: The first and most important clue is the fact that points B, D and F are midpoints of the triangle ACE. What this tells us is that point B divides line AC into two equal sides. Likewise points D and F. If point D divides line EC into two equal sides, then line ED equals

39/2 = 19.5

Also, triangle FED is similar to triangle AEC. Since ED is half of EC, and FE is half of AE. Therefore in triangles FED and AEC,

FD/ED = AC/EC

18/19.5 = AC/39

By cross multiplication we now have

(18 x 39)/19.5 = AC

702/19.5 = AC

36 = AC

Therefore line AC = 36

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