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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: 09
$\begin{array}{l}
\text{Gegeben:}\\\text{Breite} \qquad b \qquad [m] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Diagonale} \qquad d \qquad [m] \\
\\ d = \sqrt{a^{2} +b^{2} }\\ \textbf{Gegeben:} \\ b=1\frac{2}{3}m \qquad a=\frac{4}{5}m \qquad \\ \\ \textbf{Rechnung:} \\
d = \sqrt{a^{2} +b^{2} } \\
b=1\frac{2}{3}m\\
a=\frac{4}{5}m\\
d = \sqrt{(\frac{4}{5}m)^{2} +(1\frac{2}{3}m)^{2} }\\\\d=1,85m
\\\\\\ \small \begin{array}{|l|} \hline b=\\ \hline 1\frac{2}{3} m \\ \hline 16\frac{2}{3} dm \\ \hline 166\frac{2}{3} cm \\ \hline 1666\frac{2}{3} mm \\ \hline 1666666\frac{2}{3} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{4}{5} m \\ \hline 8 dm \\ \hline 80 cm \\ \hline 800 mm \\ \hline 8\cdot 10^{5} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline d=\\ \hline 1,85 m \\ \hline 18,5 dm \\ \hline 185 cm \\ \hline 1,85\cdot 10^{3} mm \\ \hline 1,85\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$