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 3inch and 5inch 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 3inch and 5inch 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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