[tex]The\ rectangle:a\ \times\ b\\\\ \left\{\begin{array}{ccc}ab=30\\2a+2b=34&/:2\end{array}\right\\\\\left\{\begin{array}{ccc}ab=30\\a+b=17\end{array}\right\\\\\left\{\begin{array}{ccc}ab=30\\a=17-b\end{array}\right\\\\substitute:\\\\(17-b)b=30[/tex]
[tex]-b^2+17b-30=0\\\\a=-1;\ b=17;\ c=-30\\\\\Delta=b^2-4ac\\\\\Delta=17^2-4\cdot(-1)\cdot(-30)=289-120=169;\ \sqrt\Delta=\sqrt{169}=13\\\\b_1=\frac{-17-13}{2\cdot(-1)}=\frac{-30}{-2}=15;\ b_2=\frac{-17+13}{2\cdot(-1)}=\frac{-4}{-2}=2\\\\a_1=17-15=2;\ a_2=17-2=15\\\\Answer:The\ rectangle:15m\ \times\ 2m.[/tex]
