To determine: The value of segment HF Given information: The following information has been given EH=7 HG=4

Formula used:
Similar triangles have sides in same ratio.
Calculation:
We know that in similar triangles HFE and FGE,
${\displaystyle \frac{HF}{FG}=\frac{FE}{GE}=\frac{HE}{FE}}$(by law of similarity)
Hence, we substitute the value of EH and HG in the equation above , we get
${\displaystyle F{E}^2=HE\left(GE\right)}$
Thus, we get
${\displaystyle FE=\sqrt{77}}$