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