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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
$\begin{array}{l}
\text{Gegeben:}\\\text{Länge} \qquad b \qquad [m] \\
\text{Diagonale} \qquad d \qquad [m] \\
\\ \text{Gesucht:} \\\text{Breite} \qquad a \qquad [m] \\
\\ a = \sqrt{d^{2} -b^{2} }\\ \textbf{Gegeben:} \\ d=\frac{1}{2}m \qquad b=\frac{2}{5}m \qquad \\ \\ \textbf{Rechnung:} \\
a = \sqrt{d^{2} -b^{2} } \\
b=\frac{2}{5}m\\
d=\frac{1}{2}m\\
a = \sqrt{(\frac{1}{2}m)^{2} -(\frac{2}{5}m)^{2} }\\\\a=\frac{3}{10}m
\\\\\\ \small \begin{array}{|l|} \hline d=\\ \hline \frac{1}{2} m \\ \hline 5 dm \\ \hline 50 cm \\ \hline 500 mm \\ \hline 5\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline \frac{2}{5} m \\ \hline 4 dm \\ \hline 40 cm \\ \hline 400 mm \\ \hline 4\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{3}{10} m \\ \hline 3 dm \\ \hline 30 cm \\ \hline 300 mm \\ \hline 3\cdot 10^{5} \mu m \\ \hline \end{array} \end{array}$