Question

Se da cubul ABCDA'B'C'D' si O centrul bazei ABCD,iar O' centrul fetei BCC'B'.
1. d(OO')

Answer 1

notam muchia cubului  =x
ducem O'M_I_BC
ducem OM_I_BC
avem triunghiul dreptunghic isoscel OMO'
O'M=OM=x/2
OO'=√[(x/2)²+(x/2)²]=√(2x²/4)=x√2/2

Answer 2

$OMO'=triunghi~dreptunghic~isoscel \\ O'M=OM= \frac{a}{2} \\ OO'= \sqrt{[( \frac{a}{2})^{2}+( \frac{a}{2})^{2} }] \to \sqrt{ \frac{2 a^{2} }{4} }=\frac{a \sqrt{2} }{2} }$
muchia cubului=a