Question

A rectangle has an area of 30 square meters and a perimeter of 34 meters. What are the dimensions of the rectangle?

Answer 1

15m x2m

Explanation:

Answer 2

`The\ rectangle:a\ *\ 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`


`-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=√(169)=13\\\\b_1=(-17-13)/(2\cdot(-1))=(-30)/(-2)=15;\ b_2=(-17+13)/(2\cdot(-1))=(-4)/(-2)=2\\\\a_1=17-15=2;\ a_2=17-2=15\\\\Answer:The\ rectangle:15m\ *\ 2m.`