Hallo Elanth,
Fläche: 44gh = a * b
Umfang: 11g + 16 h = 2a + 2b → b = 11/2 g + 8h - a
b in G1 einsetzen:
44gh = a * ( 11/2 g + 8h - a ) = 11g/2 * a + 8h * a - a2
Alle Glieder nach links bringen und zusammenfassen:
a2 - ( 8h + 11g/2 ) * a + 44gh = 0
x2 + px + q = 0
pq-Formel: p = - ( 8h + 11g/2 ) ; q = 44gh
a1,2 = - p/2 ± \(\sqrt{(p/2)^2 - q}\)
a1,2 = 4h + 11g/4 ± \(\sqrt{((4h+11g/4)^2 - 44gh}\)
a1,2 = 4h - 11g/4 ± √( 121·g2/16 - 22·g·h + 16·h2 ) = 4h -11g/4 ± √( (11g/4 - 4h)2 )
a1,2 = 4h + 11g/4 ± (11·g/4 - 4h)
a1 = 11g/2 ; a2 = 8h → b1 = 8h ; b2 = 11g/2
Gruß Wolfgang
