Question

PLEASE HELP!!

What is the value of q? Show all work. Don’t forget to label your answer.

Thank you.

Answer 1

Name this triangle ABC, where A is the angle divided into equal parts by bisector AD and point B lies under the bisector AD and point C lies over the bisector AD.

According to the bisector theorem:

`(AB)/(AC) = (BD)/(BC)`.

On the picture CD=q and BC=16, then BD=16-q.

The previous ratio becomes:

`(28)/(36) = (16-q)/(q)\\ 28q=36(16-q)\\ 28q=576-36q\\ 64q=576\\q=9`.

Answer: q=9