Question Number 218317 by Hanuda354 last updated on 06/Apr/25
Answered by mr W last updated on 06/Apr/25
$${say}\:{a}={side}\:{length}\:{of}\:{square} \\ $$$${AE}=\sqrt{{a}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} } \\ $$$${FB}={a}−\mathrm{2} \\ $$$$\frac{{FB}}{{AB}}=\frac{{AE}}{{DE}} \\ $$$$\Rightarrow\frac{{a}−\mathrm{2}}{{a}}=\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }}{\mathrm{5}} \\ $$$$\mathrm{5}\left({a}−\mathrm{2}\right)={a}\sqrt{{a}^{\mathrm{2}} −\mathrm{25}} \\ $$$$\mathrm{25}\left({a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{4}\right)={a}^{\mathrm{2}} \left({a}^{\mathrm{2}} −\mathrm{25}\right) \\ $$$${a}^{\mathrm{4}} −\mathrm{50}{a}^{\mathrm{2}} +\mathrm{100}{a}−\mathrm{100}=\mathrm{0} \\ $$$$\Rightarrow{a}\approx\mathrm{6}.\mathrm{011}\:\Rightarrow{a}^{\mathrm{2}} \approx\mathrm{36}.\mathrm{13} \\ $$
Commented by Hanuda354 last updated on 07/Apr/25
$$\mathrm{Thank}\:\mathrm{you},\:\mathrm{sir}. \\ $$