Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

Question Number 180258 by mr W last updated on 09/Nov/22

Commented by mr W last updated on 09/Nov/22

find the area of square.

$${find}\:{the}\:{area}\:{of}\:{square}. \\ $$

Answered by HeferH last updated on 09/Nov/22

((AF)/(DE)) = ((FB)/(AD)) ⇒ ((√(x^2 −9))/2) = (3/x) x^2 (x^2 −9)= 36 x^4 −9x^2 −36 = 0 (there is probably a better method)

$$\frac{{AF}}{{DE}}\:=\:\frac{{FB}}{{AD}}\:\Rightarrow\:\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{9}}}{\mathrm{2}}\:=\:\frac{\mathrm{3}}{{x}} \\ $$$$\:{x}^{\mathrm{2}} \left({x}^{\mathrm{2}} −\mathrm{9}\right)=\:\mathrm{36} \\ $$$$\:{x}^{\mathrm{4}} −\mathrm{9}{x}^{\mathrm{2}} −\mathrm{36}\:=\:\mathrm{0} \\ $$$$\:\left({there}\:{is}\:{probably}\:{a}\:{better}\:{method}\right) \\ $$$$\: \\ $$$$\: \\ $$

Commented by mr W last updated on 10/Nov/22

thanks!

$${thanks}! \\ $$

Answered by Acem last updated on 09/Nov/22

∠FAB= ∠DEA= α sin α= (3/x)= (x/( (√(x^2 +4)))) ⇒ x^4 − 9x^2 − 36= 0 ⇒ (x^2 −12) (x^2 +3)= 0 ⇒ x= 2(√3) ⇒ Surface= 12 un^2 p.s. α= (π/3)

$$\angle{FAB}=\:\angle{DEA}=\:\alpha \\ $$$$\:\mathrm{sin}\:\alpha=\:\frac{\mathrm{3}}{{x}}=\:\frac{{x}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}}\:\Rightarrow\:{x}^{\mathrm{4}} −\:\mathrm{9}{x}^{\mathrm{2}} −\:\mathrm{36}=\:\mathrm{0} \\ $$$$\Rightarrow\:\left({x}^{\mathrm{2}} −\mathrm{12}\right)\:\left({x}^{\mathrm{2}} +\mathrm{3}\right)=\:\mathrm{0} \\ $$$$\Rightarrow\:{x}=\:\mathrm{2}\sqrt{\mathrm{3}}\: \\ $$$$\Rightarrow\:{Surface}=\:\mathrm{12}\:{un}^{\mathrm{2}} \\ $$$${p}.{s}.\:\alpha=\:\frac{\pi}{\mathrm{3}} \\ $$

Commented by mr W last updated on 10/Nov/22

thanks!

$${thanks}! \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com