Question

PLEASEEEEEE HELP Given: △ABC, D∈AC m∠BDC=m∠ABC AD=7, DC=9 Find: BC, BD/BA

Answer 1

Answer:

Step-by-step explanation:

Given: △ABC, D∈AC , m∠BDC=m∠ABC , AD=7, DC=9.

Solution: Let BC=x, From the given figure and the given information, it can be seen that △ABC is similar to ΔBDC by AA rule, thus using the proportionality theorem, we get

$\frac{AC}{BC}=\frac{BC}{DC}$

⇒$\frac{16}{x}=\frac{x}{9}$

⇒$x^{2}=144$

⇒$x=12$

⇒BC=12

Now, calculate the similarity scale,

k=$\frac{AC}{BC}$

=$\frac{16}{12}=\frac{4}{3}$

Therefore, $\frac{BA}{BD}=\frac{4}{3}$

⇒$3BA=4BD$

⇒$BA=\frac{4}{3}BD$