Quandaries
and Queries 

In tirangle ABC, AB=6, BC=9, BC is the angle bisector of angle ABC and M is the midpoint of BD. If the area of ABC is 30, what is the area of ABM? The height comes out greater than the hypotenuse, but the teacher said that there's an answer for it. Can you show me how? Thanks 

Amy, There are difficulties with the statement of the problem. For one thing, if M is the midpoint of BC, then triangle ABM is half the given area of triangle ABC, and all the other information is irrelevant. (To see this, just use the formula area = (1/2) X base X height.) As for the angle bisector, BC cannot be the bisector of angle ABC  that makes no sense. Is the intended meaning that the bisector of angle ABC has length 9? Chris 

