SOLUTION: <-G----H-------I-----------J-> In the figure above, GH/HI=1/3 and HI/IJ=1/2. If the length of GI is 24, then the length of GJ is a.44 b.48 c.56 d.60 e.72

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: <-G----H-------I-----------J-> In the figure above, GH/HI=1/3 and HI/IJ=1/2. If the length of GI is 24, then the length of GJ is a.44 b.48 c.56 d.60 e.72      Log On


   

Question 907696: <-G----H-------I-----------J->
In the figure above, GH/HI=1/3 and HI/IJ=1/2. If the length of GI is 24, then the length of GJ is
a.44
b.48
c.56
d.60
e.72
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Steps done here on paper are not very neat, but I found IJ=36; and knowing the given GI=24, simply using segment addition postulate gives GI%2BIJ=24%2B36=highlight%2860%29.

Note that in my separate work not shown, the ratio relationships given can easily be converted into simple linear equations.
3GH=HI, 2HI=IJ.

Also, GH%2BHI=24
%281%2F3%29HI%2BHI=24
%284%2F3%29HI=24
HI=%283%2F4%2924
highlight_green%28HI=18%29