Question

Find the length of the segment.

Answer 1

CD = 4 , AD = 6

Explanation:

AC is an angle bisector of ∠ BAD and divides the opposite side from the angle into segments that are proportional to the other two sides, that is

`(BC)/(CD)` =
`(AB)/(AD)` ( substitute values )

`(6)/(y-1)` =
`(9)/(2y-4)` ( cross- multiply )

6(2y - 4) = 9(y - 1) ← distribute parenthesis

12y - 24 = 9y - 9 ( subtract 9y from both sides )

3y - 24 = - 9 ( add 24 to both sides )

3y = 15 ( divide both sides by 3 )

y = 5

Then

CD = y - 1 = 5 - 1 = 4

AD = 2y - 4 = 2(5) - 4 = 10 - 4 = 6