Question #7dfe9

2 Answers
Oct 7, 2016

#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#

Oct 7, 2016

#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#