Question

Question #7dfe9

Answer 1

`y = 12`

Explanation:

As `bar(BD)` is the angle bisector of `angleABC`, we have `angleABD = angleCBD`. As `angleBAD = angleBCD = 90^@` and the interior angles of any triangle sum to `180^@`, we must have `angleBDC = angleBDA`.

With that, we can use the angle-side-angle property with the shared side `bar(BD)` to say that `triangleABD ~= triangleCBD`. Equating corresponding sides, we get

`AD = CD`

`=> 3y + 6 = 5y - 18`

`=> 2y = 24`

`:. y = 12`

Answer 2

`y=12`.

Explanation:

Since, `vec(BD)` bisects `/_ABC`,

`m/_ABD=1/2m/_ABC=20^@.`

`rArr 3x-1=20^@ rArr x=7^@.`

Again, pt. `D` lies on the `/_`-bisector of `/_ABC`,

The `bot-dist.DA=bot-dist. DB`

`:. 3y+6=5y-18.`

`:. 24=2y", giving, "y=12`