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

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\[\begin{aligned} \text { Total area } & =A_{triangle}+A_{rectangle} \\\\ & =x(3 x)\left(\frac{1}{2}\right)+3 x(x+1) \\\\ & =\frac{3}{2} x^2+3 x^2+3 x \\\\ & =\frac{9}{2} x^2+3 x \end{aligned}\]

We know that

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

\[\begin{aligned}
\Rightarrow \frac{9}{2} x^2+3 x=180 \\\\
\frac{9}{2} x^2+3 x-180=0 \\\\
9 x^2+6 x-360=0 \\\\
3 x^2+2 x-120=0 \\\\
x=\frac{-2 \pm \sqrt{4-4(3)(-120)}}{2(3)} \\\\
x=\frac{-2 \pm 38}{6}=\frac{36}{6} \\\\
x=6
\end{aligned}
\]

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

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