Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

Sagot :

[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]

Answer:

15m x2m

Step-by-step explanation: