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 3- inch and 5-inch segments. Find the perimeter of the triangle in terms of x.

Answer 1

http://en.wikipedia.org/wiki/Angle_bisector_theorem

Then S/(S-x)= 5/3
and 3X=5S-5X
or 5x=3S or x=3s/5 or S=5x/3

Perimeter: (3+5)+ S+(S-x)=
8+2*5x/3 -x=
8+x(10/3-1) and you can surely simplify that.

check my thinking

Answer 2

Thought this question looked familiar, so I went back to find it and found your objection to my solution

http://www.jiskha.com/display.cgi?id=1326173456
Of course you were right to spot my error, it should have said
1.5x + 1.5x + x + 8
= 4x+8

Also just noticed a typo in bobpursley's solution
2nd line should have been
3S = 5S - 5X , then
5x = 2s
s = 5x/2 or 2.5x
perimeter = 8 + s + s-x
= 8 + 5x-x = 4x+8