[tex]\displaystyle \Delta BCD~dr\implies BD^2=BC^2+CD^2[/tex]
[tex]\displaystyle Cum~ABCD EFGH~cub\implies are~toate~laturile~egale~;~notam~lungimea \\ lor~cu~x.[/tex]
[tex]\displaystyle BD^2=x^2+x^2[/tex]
[tex]\displaystyle BD^2=2x^2[/tex]
[tex]\displaystyle BD=x\sqrt2\implies HF=x\sqrt2[/tex]
[tex]\displaystyle HFBD~dreptunghi \\ \Delta HFB~dr\implies HB^2=FB^2+HF^2 \\ HB^2=x^2+x\sqrt2^2 \\ HB^2=x^2+2x^2 \\ HB^2=3x^2 \\ HB=x\sqrt3=2\sqrt3[/tex]
