Question

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

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asked 2021-02-02
To determine: The value of segment HF
Given information:
The following information has been given
GF=6
EG=9

Answers (1)

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
\(\displaystyle{G}{F}={3}\sqrt{{{6}}}\)
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