# What is EG? FSP19610806951.jpgFSZ

What is EG?

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Ida Perry

From the figure we have

$$\displaystyle\overline{{{F}{G}}}=\overline{{{E}{F}}}$$
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 $$\displaystyle\overline{{{G}{E}}}=\overline{{{G}{H}}}+\overline{{{H}{E}}}$$
$$\displaystyle={93}+{93}$$
$$\displaystyle={186}$$
$$\displaystyle\therefore\overline{{{G}{E}}}={186}$$