Notam a, b, c si d cele patru laturi.
a+b+c+d=637 cm
Notam cu k valoarea comuna a laturilor modificate:
[tex]a- \frac{a}{13} =b- \frac{3b}{13} =c- \frac{3c}{13} =d- \frac{5d}{13} =k[/tex]
[tex] \frac{12a}{13} = \frac{10b}{13} = \frac{10c}{13} = \frac{8d}{13} =k[/tex]
a=[tex] \frac{13k}{12} [/tex]
b=c=[tex] \frac{13k}{10} [/tex]
d=[tex] \frac{13k}{8} [/tex]
Inlocuim in relatia cu perimetrul:
[tex] \frac{13k}{12} + \frac{13k}{10} + \frac{13k}{10} + \frac{13k}{8} =637 cm[/tex]
[tex] 13k( \frac{1}{12} + \frac{1}{5} + \frac{1}{8} )=13*49 [/tex]
Impartim prin 13:
k*49/120=49
k/120=1
k=120
Deci, inlocuind in relatiile care exprima laturile in functie de k:
a=13*120/12=130cm
b=c=13*120/10=156 cm
d=13*120/8=13*15=195 cm
