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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: 11
$\begin{array}{l}
\text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\
\text{Umfang} \qquad U \qquad [m] \\
\\ \text{Gesucht:} \\\text{Länge} \qquad a \qquad [m] \\
\\ a = \frac{U - 2\cdot b}{ 2}\\ \textbf{Gegeben:} \\ b=7m \qquad U=20\frac{5}{8}m \qquad \\ \\ \textbf{Rechnung:} \\
a = \frac{U - 2\cdot b}{ 2} \\
b=7m\\
U=20\frac{5}{8}m\\
a = \frac{20\frac{5}{8}m - 2\cdot 7m}{ 2}\\\\a=3\frac{5}{16}m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline U=\\ \hline 20\frac{5}{8} m \\ \hline 206\frac{1}{4} dm \\ \hline 2062\frac{1}{2} cm \\ \hline 2,06\cdot 10^{4} mm \\ \hline 2,06\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 3\frac{5}{16} m \\ \hline 33\frac{1}{8} dm \\ \hline 331\frac{1}{4} cm \\ \hline 3312\frac{1}{2} mm \\ \hline 3,31\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$