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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=(√(a^2 −5^2 )) FB=a−2 ((FB)/(AB))=((AE)/(DE)) ⇒((a−2)/a)=((√(a^2 −5^2 ))/5) 5(a−2)=a(√(a^2 −25)) 25(a^2 −4a+4)=a^2 (a^2 −25) a^4 −50a^2 +100a−100=0 ⇒a≈6.011 ⇒a^2 ≈36.13

$${say}\:{a}={side}\:{length}\:{of}\:{square} \\ $$$${AE}=\sqrt{{a}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} } \\ $$$${FB}={a}−\mathrm{2} \\ $$$$\frac{{FB}}{{AB}}=\frac{{AE}}{{DE}} \\ $$$$\Rightarrow\frac{{a}−\mathrm{2}}{{a}}=\frac{\sqrt{{a}^{\mathrm{2}} −\mathrm{5}^{\mathrm{2}} }}{\mathrm{5}} \\ $$$$\mathrm{5}\left({a}−\mathrm{2}\right)={a}\sqrt{{a}^{\mathrm{2}} −\mathrm{25}} \\ $$$$\mathrm{25}\left({a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{4}\right)={a}^{\mathrm{2}} \left({a}^{\mathrm{2}} −\mathrm{25}\right) \\ $$$${a}^{\mathrm{4}} −\mathrm{50}{a}^{\mathrm{2}} +\mathrm{100}{a}−\mathrm{100}=\mathrm{0} \\ $$$$\Rightarrow{a}\approx\mathrm{6}.\mathrm{011}\:\Rightarrow{a}^{\mathrm{2}} \approx\mathrm{36}.\mathrm{13} \\ $$

Commented by Hanuda354 last updated on 07/Apr/25

Thank you, sir.

$$\mathrm{Thank}\:\mathrm{you},\:\mathrm{sir}. \\ $$

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