回覆 19# enlighten0626 的帖子
第7題
\(\begin{align}
& A\left( 0,3 \right),B\left( 12k,5k \right),C\left( t,0 \right) \\
& \overline{OB}=13k,\overline{OC}=t,\overline{BC}=\sqrt{{{\left( 12k-t \right)}^{2}}+{{\left( 5k \right)}^{2}}} \\
& \frac{5k-3}{12k-0}=\frac{0-3}{t-0} \\
& k=\frac{3t}{5t+36} \\
& \\
& 13k+t+\sqrt{{{\left( 12k-t \right)}^{2}}+{{\left( 5k \right)}^{2}}}=30 \\
& {{\left( 30-13k-t \right)}^{2}}={{\left( 12k-t \right)}^{2}}+{{\left( 5k \right)}^{2}} \\
& 900+169{{k}^{2}}+{{t}^{2}}-780k+26kt-60t=169{{k}^{2}}-24kt+{{t}^{2}} \\
& \left( 50t-780 \right)k=60t-900 \\
& k=\frac{6t-90}{5t-78} \\
& \\
& \frac{3t}{5t+36}=\frac{6t-90}{5t-78} \\
& t=6\sqrt{6} \\
& \\
& \Delta OAC=\frac{1}{2}\times 6\sqrt{6}\times 3=9\sqrt{6} \\
\end{align}\)
