a : b = 3x : 4x = 3 : 4
Ob=140
2(3x+4x)=140
2*7x=140
14x=140
x=10
a=3x=3*10=30[m]
b=4x=4*10=40[m]
P_1=30*40=1200[m^2]
P_2=3a =3*100m^2=300m^2
\frac{P_2}{P_1}=k^2
k^2=\frac{300}{1200}
k^2=\frac{1}{4}
k=\sqrt{\frac{1}{4}}=\frac{1}{2} skala podobieństwa
a'=a*k=30*\frac{1}{2}=15[m]
b'=b*k=40*\frac{1}{2}=20[m]
Odpowiedź: wymiary 15m x 20m
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sprawdzenie:
P_2=15m*30m=300m^2=3a