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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: 03
$\begin{array}{l}
\text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\
\text{Umfang} \qquad U \qquad [m] \\
\\ \text{Gesucht:} \\\text{Länge} \qquad a \qquad [m] \\
\\ a = \frac{U - 2\cdot b}{ 2}\\ \textbf{Gegeben:} \\ b=4m \qquad U=65m \qquad \\ \\ \textbf{Rechnung:} \\
a = \frac{U - 2\cdot b}{ 2} \\
b=4m\\
U=65m\\
a = \frac{65m - 2\cdot 4m}{ 2}\\\\a=28\frac{1}{2}m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline U=\\ \hline 65 m \\ \hline 650 dm \\ \hline 6,5\cdot 10^{3} cm \\ \hline 6,5\cdot 10^{4} mm \\ \hline 6,5\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 28\frac{1}{2} m \\ \hline 285 dm \\ \hline 2,85\cdot 10^{3} cm \\ \hline 2,85\cdot 10^{4} mm \\ \hline 2,85\cdot 10^{7} \mu m \\ \hline \end{array} \end{array}$