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Question Number 176776 by cherokeesay last updated on 26/Sep/22

Answered by BaliramKumar last updated on 27/Sep/22

((3−a)/a) = (a/(4−a))  a^2  = a^2 −7a+12  a = ((12)/7)  (a^2 /(6−a^2 )) = ((24)/(25)) = ((24)/(25))×100% = 96%

$$\frac{\mathrm{3}−{a}}{{a}}\:=\:\frac{{a}}{\mathrm{4}−{a}} \\ $$$${a}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} −\mathrm{7}{a}+\mathrm{12} \\ $$$${a}\:=\:\frac{\mathrm{12}}{\mathrm{7}} \\ $$$$\frac{{a}^{\mathrm{2}} }{\mathrm{6}−{a}^{\mathrm{2}} }\:=\:\frac{\mathrm{24}}{\mathrm{25}}\:=\:\frac{\mathrm{24}}{\mathrm{25}}×\mathrm{100\%}\:=\:\mathrm{96\%} \\ $$

Commented by cherokeesay last updated on 26/Sep/22

Nice ! thank you !

$${Nice}\:!\:{thank}\:{you}\:! \\ $$

Answered by a.lgnaoui last updated on 26/Sep/22

x=cote du care   aire=x^2   aire de partie bleu=(((4−x))/2)x+(((3−x))/2)x=((7x)/2)−x^2   aire totale=((4×3)/2)=6  ⇒((7x)/2)−x^2 =6−x^2   x=((12)/7)  ((aire jaune)/(aire bleu))=(x^2 /(6−x^2 ))=((24)/(25))=96%

$${x}={cote}\:{du}\:{care}\:\:\:{aire}={x}^{\mathrm{2}} \\ $$$${aire}\:{de}\:{partie}\:{bleu}=\frac{\left(\mathrm{4}−{x}\right)}{\mathrm{2}}{x}+\frac{\left(\mathrm{3}−{x}\right)}{\mathrm{2}}{x}=\frac{\mathrm{7}{x}}{\mathrm{2}}−{x}^{\mathrm{2}} \\ $$$${aire}\:{totale}=\frac{\mathrm{4}×\mathrm{3}}{\mathrm{2}}=\mathrm{6}\:\:\Rightarrow\frac{\mathrm{7}{x}}{\mathrm{2}}−{x}^{\mathrm{2}} =\mathrm{6}−{x}^{\mathrm{2}} \:\:{x}=\frac{\mathrm{12}}{\mathrm{7}} \\ $$$$\frac{{aire}\:{jaune}}{{aire}\:{bleu}}=\frac{{x}^{\mathrm{2}} }{\mathrm{6}−{x}^{\mathrm{2}} }=\frac{\mathrm{24}}{\mathrm{25}}=\mathrm{96\%} \\ $$

Commented by cherokeesay last updated on 26/Sep/22

Great ! thank you

$${Great}\:!\:{thank}\:{you} \\ $$

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