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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: 05
$\begin{array}{l}
\text{Gegeben:}\\\text{Umfang} \qquad U \qquad [m] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\
\\ b = \frac{U - 2\cdot a}{ 2}\\ \textbf{Gegeben:} \\ U=19m \qquad a=1m \qquad \\ \\ \textbf{Rechnung:} \\
b = \frac{U - 2\cdot a}{ 2} \\
U=19m\\
a=1m\\
b = \frac{19m - 2\cdot 1m}{ 2}\\\\b=8\frac{1}{2}m
\\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline U=\\ \hline 19 m \\ \hline 190 dm \\ \hline 1,9\cdot 10^{3} cm \\ \hline 1,9\cdot 10^{4} mm \\ \hline 1,9\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 8\frac{1}{2} m \\ \hline 85 dm \\ \hline 850 cm \\ \hline 8,5\cdot 10^{3} mm \\ \hline 8,5\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$