SOLUTION: In triangle ABC, side AB is x longer than side BC . The ray bisecting angle B intersects side AC at point D. If AC = 8 and CD = 3, find the perimeter of the triangle in terms of x.

Algebra ->  Triangles -> SOLUTION: In triangle ABC, side AB is x longer than side BC . The ray bisecting angle B intersects side AC at point D. If AC = 8 and CD = 3, find the perimeter of the triangle in terms of x.      Log On


   

Question 388450: In triangle ABC, side AB is x longer than side BC . The ray bisecting angle B intersects side AC at point D. If AC = 8 and CD = 3, find the perimeter of the triangle in terms of x.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
From The given, AB = x + BC. Also, again from the given we know that CD = 3 and AD = 5. Now using a result from Euclidean geometry stating that (CD)*(AB) = (BC)*(AD) if BD is the angle bisector of angle B, we get 3(x + BC) = 5*BC, or 3x = 2*BC, or BC = 3x/2. Then the perimeter of the triangle is 3x/2 + 5x/2 + 8 = 4x + 8.