NMMRUS 90 Loesung
Wie breit muss der Streifen sein?
Also, das Feld hat die Länge L und die Breite B - die gesuchte Breite des Streifens sei x. Die ungemähte Fläche (die in der Mitte über bleibt) ist L-2x lang und B-2x breit. Die Fläche in der Mitte soll genau halb so groß sein, wie die Fläche des gesamten Feldes.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {{L\cdot B} \over 2} = (L - 2x)\cdot (B - 2x)}
Bevor wir weiterrechnen - eine kleine (sicher einsichtige) Bedingung:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B > 2x}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L > 2x}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {{L\cdot B} \over 2} = L\cdot B -2x\cdot (L + B) + 4x^2}
Weil ich mir die "große" Formel für die quadratische Gleichung nicht merken kann dividiere ich jetzt durch 4.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 - {{L + B}\over 2}\cdot x + {{L\cdot B \over 8}} = 0}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{1,2} = {{L + B}\over 4} \pm \sqrt{({{L + B}\over 4})^2 - {{L\cdot B \over 8}}}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x_{1,2} = {{L + B}\over 4} \pm \sqrt{{L^2+2\cdot L\cdot B+B^2 -2\cdot L\cdot B}\over 16}}