Zad. 6
[tex]a) \\d=6\sqrt2\\d^2+H^2=D^2\\D^2=(6\sqrt2)^2+10^2\\D^2=72+100\\D^2=172\\D=\sqrt{172}=2\sqrt{43}\\\\b) \\D^2=5^2+9^2\\D^2=25+81\\D^2=106\\D=\sqrt{106}\\\\c)\\\\D^2=(2*4)^2+8^2\\D^2=8^2+8^2\\D^2=2*64\\D=8\sqrt2[/tex]
Zad. 7
a)
[tex]D^2=d^2+a^2\\a=10\\d=10\sqrt2\\D^2=(10\sqrt2)^2+10^2\\D^2=100*2+100\\D^2=200+100\\D^2=300\\D=10\sqrt3[/tex]
b)
[tex]D^2=d^2+a^2\\D^2=(a\sqrt2)^2+a^2\\D^2=2a^2+a^2\\D^2=3a^2\\\underline{D=a\sqrt3}[/tex]
c)
[tex]a\sqrt3=10cm /:\sqrt3\\a=\frac{10}{\sqrt3}cm=\frac{10\sqrt3}3cm\\\\\text{Kostka rubika ma krawedz dlugosci } \frac{10\sqrt3}3cm[/tex]
