BC=6
EB=6√2 (diagonala unei fete a cubului)
EC=6√3 (diagonala cubului)
ducem BM_I_ EC
EM=x
MC=6√3-x
BM²=EB²-x² =(6√2)²-x² =72-x²
BM²=BC²-(6√3-x)²=6²-(6√3-x)²=36-108+12√3x-x²=12√3x-72-x²
72-x²=12√3x-72-x²
72=12√3x-72
12√3x=144
x=144/12√3=12/√3=12√3/3=4√3 cm
BM²=72-(4√3)²=72-48=24
BM=2√6 cm
