keliling alas sebuah kubus adalah 16cm maka panjang diagonal ruang kubus adalah .... cm

Panjang sisi alas :

[tex]k = s {}^{2} \\ 16 = s {}^{2} \\ s = \sqrt{16} \\ s = 4 \: cm[/tex]

Panjang diagonal alas :

[tex]x {}^{2} = 4 {}^{2} + 4 {}^{2} \\ x {}^{2} = 16 + 16 \\ x {}^{2} = 32 \\ x = \sqrt{32} \\ x = 4 \sqrt{2} \: cm[/tex]

Panjang diagonal ruang :

[tex]x {}^{2} = (4 \sqrt{2} ) {}^{2} + 4 {}^{2} \\ x {}^{2} = (16 \times 2) + 16 \\ x {}^{2} = 32 + 16 \\ x {}^{2} = 48 \\ x = \sqrt{48} \\ x = 4 \sqrt{3} \: cm[/tex]

SEMOGA MEMBANTU :)