Posted by **Anonymous** on Tuesday, January 10, 2012 at 12:30am.

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. ( triangle angle bisector theorem)

- Geometry -
**Reiny**, Tuesday, January 10, 2012 at 1:12am
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**, Tuesday, January 10, 2012 at 9:31pm
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 3-inch and 5-inch segments. Find the perimeter of the triangle in terms of x.

- Geometry -
**GeoGeo**, Tuesday, January 29, 2013 at 7:28pm
Anonymous is correct, for the answer is 4x+8.

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