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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: 10
$\begin{array}{l}
\text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Umfang} \qquad U \qquad [m] \\
\\ U = 2\cdot a + 2\cdot b\\ \textbf{Gegeben:} \\ b=1\frac{1}{6}m \qquad a=\frac{11}{17}m \qquad \\ \\ \textbf{Rechnung:} \\
U = 2\cdot a + 2\cdot b \\
b=1\frac{1}{6}m\\
a=\frac{11}{17}m\\
U = 2\cdot \frac{11}{17}m + 2\cdot 1\frac{1}{6}m\\\\U=3\frac{32}{51}m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{1}{6} m \\ \hline 11\frac{2}{3} dm \\ \hline 116\frac{2}{3} cm \\ \hline 1166\frac{2}{3} mm \\ \hline 1166666\frac{2}{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{11}{17} m \\ \hline 6\frac{8}{17} dm \\ \hline 64\frac{12}{17} cm \\ \hline 647\frac{1}{17} mm \\ \hline 647058\frac{14}{17} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline U=\\ \hline 3\frac{32}{51} m \\ \hline 36\frac{14}{51} dm \\ \hline 362\frac{38}{51} cm \\ \hline 3627\frac{23}{51} mm \\ \hline 3627450\frac{50}{51} \mu m \\ \hline \end{array} \end{array}$