Geometrie-Viereck-Rechteck

$A = a\cdot b$
1 2 3 4 5 6 7 8 9 10 11 12
$a = \frac{A}{b}$
1 2 3 4 5
$b = \frac{A}{a}$
1 2 3 4 5 6 7 8 9 10 11 12 13
$U = 2\cdot a + 2\cdot b$
1 2 3 4 5 6 7 8 9 10 11 12 13
$a = \frac{U - 2\cdot b}{ 2}$
1 2 3 4 5 6 7 8 9 10 11
$b = \frac{U - 2\cdot a}{ 2}$
1 2 3 4 5 6 7 8 9 10 11 12
$d = \sqrt{a^{2} +b^{2} }$
1 2 3 4 5 6 7 8 9 10 11 12
$b = \sqrt{d^{2} -a^{2} }$
1 2 3 4 5 6 7 8 9 10
$a = \sqrt{d^{2} -b^{2} }$
1 2 3 4 5 6 7 8 9 10
Beispiel Nr: 12
$\begin{array}{l} \text{Gegeben:}\\\text{Umfang} \qquad U \qquad [m] \\ \text{Länge} \qquad a \qquad [m] \\ \\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\ \\ b = \frac{U - 2\cdot a}{ 2}\\ \textbf{Gegeben:} \\ U=\frac{5}{9}m \qquad a=\frac{1}{2}m \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{U - 2\cdot a}{ 2} \\ U=\frac{5}{9}m\\ a=\frac{1}{2}m\\ b = \frac{\frac{5}{9}m - 2\cdot \frac{1}{2}m}{ 2}\\\\b=-\frac{2}{9}m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline \frac{1}{2} m \\ \hline 5 dm \\ \hline 50 cm \\ \hline 500 mm \\ \hline 5\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline U=\\ \hline \frac{5}{9} m \\ \hline 5\frac{5}{9} dm \\ \hline 55\frac{5}{9} cm \\ \hline 555\frac{5}{9} mm \\ \hline 555555\frac{5}{9} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline -\frac{2}{9} m \\ \hline -2\frac{2}{9} dm \\ \hline -22\frac{2}{9} cm \\ \hline -222\frac{2}{9} mm \\ \hline -222222\frac{2}{9} \mu m \\ \hline \end{array} \end{array}$