In triangle \(ABC\), \(AB=16\), \(AC=24\), \(BC=19\), and \(AD\) is an angle bisector. Find the ratio of the area of triangle \(ABD\) to the area of triangle \(ACD\). (Express your answer as a fraction in lowest terms.)

benjamingu22
Jul 23, 2017

#1**+1 **

Both triangles are under the same height...so their areas will be to each other as their bases

And since angle BAC is bisected, bases BD and CD will have the same relationship as their adjacent sides....i.e., 16/24....so the areas of triangles ABD and ACD wii have the same ratio......that is :

area ABD /area of ACD = 16 / 24 = 2 / 3

Here's a pic :

CPhill
Jul 23, 2017