\(\displaystyle{S}\frac{{G}}{{S}}{F}=\frac{{24}}{{{24}+{30}}}=\frac{{24}}{{54}}=\frac{{4}}{{9}}\)

\(\displaystyle{S}\frac{{H}}{{S}}{E}=\frac{{26}}{{{26}+{32.5}}}=\frac{{26}}{{58.5}}=\frac{{4}}{{9}}\)

Since,

\(\displaystyle\triangle{G}{S}{H}{\quad\text{and}\quad}\triangle{F}{S}{E}\) share \(\displaystyle\angle{S}\), and \(\displaystyle{S}\frac{{G}}{{S}}{F}={S}\frac{{H}}{{S}}\)E, then \(\displaystyle\triangle{G}{S}{H}\sim\triangle{F}{S}{E}\) by SAS. Thus:

\(\displaystyle{H}\frac{{G}}{{E}}{F}={S}\frac{{G}}{{S}}{F}\)

\(\displaystyle\frac{{20}}{{E}}{F}=\frac{{4}}{{9}}\)

\(\displaystyle{E}{F}=\frac{{{20}\times{9}}}{{4}}\)

EF=45m

\(\displaystyle{S}\frac{{H}}{{S}}{E}=\frac{{26}}{{{26}+{32.5}}}=\frac{{26}}{{58.5}}=\frac{{4}}{{9}}\)

Since,

\(\displaystyle\triangle{G}{S}{H}{\quad\text{and}\quad}\triangle{F}{S}{E}\) share \(\displaystyle\angle{S}\), and \(\displaystyle{S}\frac{{G}}{{S}}{F}={S}\frac{{H}}{{S}}\)E, then \(\displaystyle\triangle{G}{S}{H}\sim\triangle{F}{S}{E}\) by SAS. Thus:

\(\displaystyle{H}\frac{{G}}{{E}}{F}={S}\frac{{G}}{{S}}{F}\)

\(\displaystyle\frac{{20}}{{E}}{F}=\frac{{4}}{{9}}\)

\(\displaystyle{E}{F}=\frac{{{20}\times{9}}}{{4}}\)

EF=45m