# exo45.tex

%@Auteur: François Meria
%@Dif:3
On donne les résultats suivants en rappelant que $a^2$
signifie $a\times a$ :
\begin{center}
$\begin{array}{|*{11}{c|}} \hline a & 1 & 2 & 3 & 4 & {\bf 5} & 6 & 7 & 8 & {\bf 9} & {\bf 10} \\ \hline a^2 & 1 & 4 & 9 & 16 & {\bf 25} & 36 & 49 & 64 & {\bf 81} & {\bf 100} \\ \hline \end{array}$
\par\vspace{5mm}\par
$\begin{array}{|*{11}{c|}} \hline a & 11 & 12 & {\bf 13} & 14 & 15 & 16 & 17 & 18 & 19 & 20 \\ \hline a^2 & 121 & 144 & {\bf 169} & 196 & 225 & 256 & 289 & 324 & 361 & 400 \\ \hline \end{array}$
\end{center}
Dans chacun des cas suivants, calculer la longueur inconnue :
\begin{multicols}{3}
\begin{myenumerate}
\item\subitem{}\par
\begin{tabular}{lc}
$\left\{ \begin{array}{l} AC=3 \\ AB=4 \\ BC=x\\ \end{array} \right.$ & \psset{unit=0.75}
\begin{pspicture}(0,+1.2)(2,3.2)
\pstTriangle[PointSymbol=none](0,0){A}(2,0){C}(0,3){B}
\pstRightAngle{C}{A}{B}
\put(1.2,1.6){$x$}
\end{pspicture}
\end{tabular}
\par\vspace{1cm}\par
\item\subitem{}\par
\begin{tabular}{lc}
$\left\{ \begin{array}{l} AC=6 \\ AB=8 \\ BC=x\\ \end{array} \right.$ & \psset{unit=0.75}
\begin{pspicture}(0,+1.2)(2,3.2)
\pstTriangle[PointSymbol=none](0,0){A}(2,0){C}(0,3){B}
\pstRightAngle{C}{A}{B}
\put(1.2,1.6){$x$}
\end{pspicture}
\end{tabular}
\par\vspace{1cm}\par
\item\subitem{}\par
\begin{tabular}{lc}
$\left\{ \begin{array}{l} AC=4,8 \\ AB=1,4 \\ BC=x\\ \end{array} \right.$ & \psset{unit=0.75}
\begin{pspicture}(0,1.2)(2,3.2)
\pstTriangle[PointSymbol=none](0,1){A}(3.2,1){C}(0,2.5){B}
\pstRightAngle{C}{A}{B}
\put(1.4,2.1){$x$}
\end{pspicture}
\end{tabular}
\par\vspace{1cm}\par
\item\subitem{}\par
\begin{tabular}{lc}
$\left\{ \begin{array}{l} AC=12 \\ AB=5 \\ BC=x\\ \end{array} \right.$ & \psset{unit=0.75}
\begin{pspicture}(0,1.2)(2,3.2)
%\psgrid
\pstTriangle[PointSymbol=none](0,1){A}(3.2,1){C}(0,2.5){B}
\pstRightAngle{C}{A}{B}
\put(1.4,2.1){$x$}
\end{pspicture}
\end{tabular}
\par\vspace{1cm}\par
\item\subitem{}\par
\begin{tabular}{lc}
$\left\{ \begin{array}{l} AC=x \\ AB=40 \\ BC=41\\ \end{array} \right.$ & \psset{unit=0.75}
\begin{pspicture}(0,+1.2)(2,3.2)
\pstTriangle[PointSymbol=none](0,0){A}(2,0){C}(0,3){B}
\pstRightAngle{C}{A}{B}
\put(0.95,-0.4){$x$}
\end{pspicture}
\end{tabular}
\par\vspace{1cm}\par
\item\subitem{}\par
\begin{tabular}{lc}
$\left\{ \begin{array}{l} AC=1 \\ AB=2 \\ BC=x\\ \end{array} \right.$ & \psset{unit=0.75}
\begin{pspicture}(0,+1.2)(2,3.2)
\pstTriangle[PointSymbol=none](0,0){A}(2,0){C}(0,3){B}
\pstRightAngle{C}{A}{B}
\put(1.2,1.6){$x$}
\end{pspicture}
\end{tabular}
\end{myenumerate}
\end{multicols}