Question 388450
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.