Question

HELP PLEASE! What is BD??

Answer 1

`BD=13`

Explanation:

Note that Ray AC bisects ∠A. Therefore, we can use the Angle Bisector Theorem shown below.

Hence:

`\displaystyle (27)/(x+5)=(12)/(x)`

Solve for x. Cross-multiply:

`12(x+5)=27(x)`

Distribute:

`12x+60=27x`

Subtract 12x from both sides:

`15x=60`

Divide both sides by 15. Thus:

`x=4`

BD is the sum of BC and CD:

`BD=BC+CD`

Substitute:

`BD=x+(x+5)`

Substitute and evaluate:

`BD=(4)+(4+5)=13`

Therefore, BD is 13.