Answer:
DC = 3
Step-by-step explanation:
Based on triangle similarity theorem, we would have the following equation:
[tex] \frac{AD}{AC} = \frac{AE}{AB} [/tex]
Plug in the values
[tex] \frac{9}{9 + DC} = \frac{12}{12 + 4} [/tex]
[tex] \frac{9}{9 + DC} = \frac{12}{16} [/tex]
[tex] \frac{9}{9 + DC} = \frac{3}{4} [/tex]
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
