Posted by Anonymous on .
One side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3inch and 5inch segments. Find the perimeter of the triangle in terms of x. ( triangle angle bisector theorem)

Geometry 
Reiny,
let the shorter side be a, then the longer side is a+x
by the Triangle Angle Bisector Theorm
(a+x)/5 = a/3
3a + 3x = 5a
3x = 2a
a = 3x/2 = 1.5x
so the sum of the three sides
= a + a+x + 8
= 1.5x + x + 8
= 2.5x + 8 
Geometry 
Anonymous,
Reiny, if a+a+x+8 then how come it is 1.5x+x+8=2.5x+8? I thought that it is 1.5x+1.5x+x+8=4x+8. Previous problem:one side of a triangle is x inches longer than another side. The ray bisecting the angle formed by these sides divides the opposite side into 3inch and 5inch segments. Find the perimeter of the triangle in terms of x.

Geometry 
GeoGeo,
Anonymous is correct, for the answer is 4x+8.