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$\begin{cases}
\displaystyle h^2=170-x^2=194-y^2 \\
\displaystyle x+y=\sqrt{656}
\end{cases}$
$\begin{cases}
\displaystyle x=\frac{79}{\sqrt{41}} \\
\displaystyle y=\frac{85}{\sqrt{41}}
\end{cases}$
$\displaystyle h=\frac{27\sqrt{41}}{41}$
$\displaystyle A=\frac{(x+y)h}{2}=\frac{4\sqrt{41}\cdot 27\sqrt{41}}{2\cdot 41}=54$
Che se poi sviluppiamo le formule, otteniamo:
$\begin{cases}
\displaystyle h^2=a^2-x^2=b^2-y^2 \\
\displaystyle x+y=c
\end{cases}$
$\begin{cases}
\displaystyle a^2-x^2=b^2-(c-x)^2 \\
\displaystyle y=c-x
\end{cases}$
$\displaystyle x=\frac{a^2-b^2+c^2}{2c}$
$\displaystyle h=\sqrt{a^2-\frac{(a^2-b^2+c^2)^2}{4c^2}}$
$\displaystyle A=\frac{ch}{2}=\frac12\sqrt{a^2c^2-\frac{(a^2-b^2+c^2)^2}{4}}$
E bravo il nostro Qin Jiushao
