[tex]area \ of \ a \ rectangle : \ A= 385 \ cm^2\\perimeter : P= 92 cm\\ length : \ l\\ width: \ w \\ \\ P=2l + 2w \\ A=l\cdot w\\\\ 92=2l + 2w \ \ / :2\\ 385=l\cdot w[/tex]
[tex]46= l + w \\ 385=l\cdot w \\\\l=46-w \\ 385=w(46-w)\\\\385= 46w-w^2 \\ \\ w^2- 46w+385 =0[/tex]
[tex]a=1, \ \ \ b=-46, \ \ \ c=385 \\\\ quardic \ formula : \\\\ w_{1}=\frac{-b-\sqrt{b^2-4ac}}{2a} =\frac{46-\sqrt{ (-46)^2-4 \cdot 1\cdot 385}}{2 }= \frac{46-\sqrt{2116-1540}}{2 }=\\\\=\frac{46-\sqrt{2116-1540}}{2 }=\frac{46-\sqrt{576}}{2}= \frac{46-24}{2}=\frac{22}{2} = 11 \ cm[/tex]
[tex]w_{2}=\frac{-b+\sqrt{b^2-4ac}}{2a} = \frac{46+24}{2}=\frac{70}{2} = 35 \ cm \\\\w_{1}= 11 \ cm\ \ \\ l_{1}=46-11 =35 \ cm \\ \\ or \\\\ w_{2}=35 \ cm \\l_{2} =46-35=11 \ cm[/tex]
