Question

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)

Answer 1

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

Answer 2

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.

Answer 3

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