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

$\begin{gathered} EF\colon FG=4\colon1=\frac{4}{4+1}=\frac{4}{5} \\ FG\colon GH=1\colon5=\frac{1}{1+6}=\frac{1}{7} \\ EF\colon GH=4\colon5=\frac{4}{4+5}=\frac{4}{9} \end{gathered}$

Now:

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