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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
$\begin{array}{l}
\text{Gegeben:}\\\text{Fläche} \qquad A \qquad [m^{2}] \\
\text{Länge} \qquad a \qquad [m] \\
\\ \text{Gesucht:} \\\text{Breite} \qquad b \qquad [m] \\
\\ b = \frac{A}{a}\\ \textbf{Gegeben:} \\ A=\frac{5}{12}m^{2} \qquad a=-\frac{6}{19}m \qquad \\ \\ \textbf{Rechnung:} \\
b = \frac{A}{a} \\
A=\frac{5}{12}m^{2}\\
a=-\frac{6}{19}m\\
b = \frac{\frac{5}{12}m^{2}}{-\frac{6}{19}m}\\\\b=-1\frac{23}{72}m
\\\\\\ \small \begin{array}{|l|} \hline A=\\ \hline \frac{5}{12} m^2 \\ \hline 41\frac{2}{3} dm^2 \\ \hline 4166\frac{2}{3} cm^2 \\ \hline 416666\frac{2}{3} mm^2 \\ \hline 0,00417 a \\ \hline 4,17\cdot 10^{-5} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline -\frac{6}{19} m \\ \hline -3\frac{3}{19} dm \\ \hline -31\frac{11}{19} cm \\ \hline -315\frac{15}{19} mm \\ \hline -315789\frac{9}{19} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline -1\frac{23}{72} m \\ \hline -13\frac{7}{36} dm \\ \hline -131\frac{17}{18} cm \\ \hline -1319\frac{4}{9} mm \\ \hline -1319444\frac{4}{9} \mu m \\ \hline \end{array} \end{array}$