Question

The points E, F, G and H all lie on the same line segment, in that order, such that the ratio of EF: FG : GH is equal to 4:1:5. If EH = 10, find EG.

Answer 1

`\begin{gathered} EF\colon FG=4\colon1=(4)/(4+1)=(4)/(5) \\ FG\colon GH=1\colon5=(1)/(1+6)=(1)/(7) \\ EF\colon GH=4\colon5=(4)/(4+5)=(4)/(9) \end{gathered}`

Now:

`\begin{gathered} EH=EF+FG+GH \\ 10=(4)/(5)FG+7FG+(4)/(9)\cdot7FG \\ 10=(491)/(45)FG \\ FG=(450)/(491) \end{gathered}`
`\begin{gathered} EF=(4)/(5)FG=(360)/(491) \\ EG=EF+FG=(450)/(491)+(360)/(491)\approx1.649694 \end{gathered}`