Question

# To determine: The value of segment HF Given information: The following information has been given GF=6 EG=9

Similarity
To determine: The value of segment HF
Given information:
The following information has been given
GF=6
EG=9

2021-02-03
Calculation:
We know that in similar triangles FGE and HGF,
$$\displaystyle\frac{{{F}{G}}}{{{H}{G}}}=\frac{{{G}{E}}}{{{G}{F}}}=\frac{{{F}{E}}}{{{H}{F}}}$$(by law of similarity)
Hence, we substitute the value of EH and HG in the equation above, we get
$$\displaystyle{G}{F}^{{2}}={G}{E}{\left({H}{G}\right)}$$
Thus, we get
$$\displaystyle{G}{F}={3}\sqrt{{{6}}}$$