Question

HELP !!111!

In triangle ABC segment DE is parallel to the side AC . (The endpoints of segment DE lie on the sides AB and BC respectively). Find the ratio AD:BD, if AC:DE=55:28

Answer 1

AD/DB = 27/28

Explanation:

We are to find AD: BD

We can solve this problem using proportions. Putting the larger triangle over the smaller triangle and using similar triangles we know

AB AC

-------- = -----------

DB DE

AB 55

-------- = -----------

DB 28

We can rewrite

AB as AD + DB since it is a line

AD +DB 55

----------- = -----------

DB 28

Using cross products

28 (AD +DB) = 55 DB

Distribute

28 AD +28DB = 55 DB

Subtract 28 DB from each side

28 AD +28DB- 28DB = 55 DB -28DB

28AD = 27DB

We want the ratio AD/DB

Divide by DB

28AD/DB = 27DB/DB

28AD/DB = 27

Divide by 28

28AD/28DB = 27/28

AD/DB = 27/28