## Determine the length and width of the rectangular region of the house

Home -> Solved problems -> Determine the length and width of the rectangular region of the house

### Solution

We know that

\[\begin{aligned}
\text { Total area } & =180
\end{aligned}\]

\Rightarrow \frac{9}{2} x^2+3 x=180 \\\\

\frac{9}{2} x^2+3 x-180=0 \\\\

9 x^2+6 x-360=0 \\\\

3 x^2+2 x-120=0 \\\\

x=\frac{-2 \pm \sqrt{4-4(3)(-120)}}{2(3)} \\\\

x=\frac{-2 \pm 38}{6}=\frac{36}{6} \\\\

x=6

\end{aligned}

\]

Home -> Solved problems -> Determine the length and width of the rectangular region of the house

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