Question Number 153082 by liberty last updated on 04/Sep/21
Answered by Rasheed.Sindhi last updated on 04/Sep/21
$$\frac{{L}}{{W}}=\frac{{W}}{{L}−{W}}\Rightarrow{L}^{\mathrm{2}} −{LW}={W}^{\mathrm{2}} \\ $$$$\Rightarrow\left(\frac{{L}}{{W}}\right)^{\mathrm{2}} −\frac{{L}}{{W}}−\mathrm{1}=\mathrm{0} \\ $$$$\frac{{L}}{{W}}=\frac{\mathrm{1}\pm\sqrt{\mathrm{1}−\mathrm{4}\left(−\mathrm{1}\right)}}{\mathrm{2}}=\frac{\mathrm{1}\pm\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$${Negative}\:{value}\:{rejected} \\ $$$$\frac{{L}}{{W}}=\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$ \\ $$