Point H is on line segment \overline{GI} GI . Given GI=5x,GI=5x, HI=3x-8,HI=3x−8, and GH=3x,GH=3x, determine the numerical length of \overline{GH}. GH .

Answer 1

By segment addition postulate GH + HI = GI

substituting given expressions for those segments:

3x + 3x - 8 = 5x

6x - 8 = 5x

x = 8

GH = 3*8 = 24

HI = 3x - 8 = 3*8 - 8 = 16

GI = 5x = 5*8 = 40