What is EG? FSP19610806951.jpgFSZ

Sheelmgal1p 2021-11-26 Answered
What is EG?
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Ida Perry
Answered 2021-11-27 Author has 8525 answers

From the figure we have
image
\(\displaystyle\overline{{{F}{G}}}=\overline{{{E}{F}}}\)
and \(\displaystyle\angle{G}{H}{F}={90}°\)
\(\displaystyle\Rightarrow\angle{E}{H}{F}={90}°\)
also \(\displaystyle\overline{{{G}{H}}}={93}\) units
Since \(\triangle GHF\) is right angle triangle, hence
\(\displaystyle\overline{{{G}{H}}}^{{2}}+\overline{{{H}{F}}}^{{2}}=\overline{{{G}{F}}}^{{2}}\)
\(\displaystyle{93}^{{2}}+\overline{{{H}{F}}}^{{2}}=\overline{{{G}{F}}}^{{2}}\)
\(\displaystyle\overline{{{G}{F}}}^{{2}}-\overline{{{H}{F}}}^{{2}}={93}^{{2}}\)-(1)
Also since \(\triangle FHE\) is right angle triangle, hence
\(\displaystyle\overline{{{F}{H}}}^{{2}}+\overline{{{H}{E}}}^{{2}}=\overline{{{E}{F}}}^{{2}}\)
\(\displaystyle\overline{{{H}{E}}}^{{2}}=\overline{{{E}{F}}}^{{2}}-\overline{{{F}{H}}}^{{2}}\)
\(\displaystyle=\overline{{{G}{F}}}^{{2}}-\overline{{{H}{F}}}^{{2}}\)
\(\displaystyle={93}^{{2}}\), using (1)
\(\displaystyle\therefore\overline{{{H}{F}}}={93}\)
Therefore \(\displaystyle\overline{{{G}{E}}}=\overline{{{G}{H}}}+\overline{{{H}{E}}}\)
\(\displaystyle={93}+{93}\)
\(\displaystyle={186}\)
\(\displaystyle\therefore\overline{{{G}{E}}}={186}\)

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