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

To determine: The value of segment HF
Given information:
The following information has been given
EH=7
HG=4
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Bentley Leach
Formula used:
Similar triangles have sides in same ratio.
Calculation:
We know that in similar triangles HFE and FGE,
$\frac{HF}{FG}=\frac{FE}{GE}=\frac{HE}{FE}$(by law of similarity)
Hence, we substitute the value of EH and HG in the equation above , we get
$F{E}^{2}=HE\left(GE\right)$
Thus, we get
$FE=\sqrt{77}$