Question

Using Triangle Similarity Theorems (6)

A
12
E A
B
9
D
What is the length of DC? Show work.

Answer 1

DC = 3

Explanation:

Based on triangle similarity theorem, we would have the following equation:

`(AD)/(AC) = (AE)/(AB)`

Plug in the values

`(9)/(9 + DC) = (12)/(12 + 4)`

`(9)/(9 + DC) = (12)/(16)`

`(9)/(9 + DC) = (3)/(4)`

Cross multiply

3(9 + DC) = 9×4

27 + 3DC = 36

Subtract 27 from each side

3DC = 36 - 27

3DC = 9

Divide both sides by 3

DC = 9/3

DC = 3