Question

Given the diagram below with line DE║ line AC. Find BC.

Answer 1

Answer:

13.5

Step-by-step explanation:

In triangle ABC, DE || AC

Therefore by basic proportionality theorem:

$\frac{BD}{DA} = \frac {BE}{EC} \\\\\therefore \frac{4}{8} = \frac {BE}{9} \\\\\therefore \frac{1}{2} = \frac {BE}{9} \\\\\therefore BE = \frac{9}{2} \\\\\therefore BE = 4.5\\\because BC = BE + EC \\\therefore BC = 4.5 + 9\\\huge \red {\boxed {\therefore BC = 13.5}}$