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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: 13
$\begin{array}{l}
\text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Umfang} \qquad U \qquad [m] \\
\\ U = 2\cdot a + 2\cdot b\\ \textbf{Gegeben:} \\ b=1\frac{1}{3}m \qquad a=1\frac{6}{7}m \qquad \\ \\ \textbf{Rechnung:} \\
U = 2\cdot a + 2\cdot b \\
b=1\frac{1}{3}m\\
a=1\frac{6}{7}m\\
U = 2\cdot 1\frac{6}{7}m + 2\cdot 1\frac{1}{3}m\\\\U=6\frac{8}{21}m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{1}{3} m \\ \hline 13\frac{1}{3} dm \\ \hline 133\frac{1}{3} cm \\ \hline 1333\frac{1}{3} mm \\ \hline 1333333\frac{1}{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 1\frac{6}{7} m \\ \hline 18\frac{4}{7} dm \\ \hline 185\frac{5}{7} cm \\ \hline 1857\frac{1}{7} mm \\ \hline 1857142\frac{6}{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline U=\\ \hline 6\frac{8}{21} m \\ \hline 63\frac{17}{21} dm \\ \hline 638\frac{2}{21} cm \\ \hline 6380\frac{20}{21} mm \\ \hline 6380952\frac{8}{21} \mu m \\ \hline \end{array} \end{array}$