Explicație pas cu pas:
Fie BC=2x => AM=2xV3/2 => AM=xV3 cm
M mij BC => VM _|_ BC
VM mediana => BM=MC=x cm
In triunghiul VMB
mM=90
BM=x cm
VB=6V2 cm
=> T.P VM^2=VB^2-BM^2 => VM^2=72-x²
In triunghiul VAM
mV=90
AM=xV3 cm
AV=6V2 cm
VM²=72-x²
=> T.P AM²=AV²+VM² => 3x²=72+72-x² => 4x²=2*72 =>x²=2*18 => x=6cm => AB=BC=AC=12cm
In triunghiul VAB
=> R.T.P AB²=2VB²=>144=144 (A) =>
AV_|_VB
AV_|_VM
VM n VB =/= Ø
=> AV_|_(VBM)
Fie MQ_|_VB
MQ_|_AV (AV_|_(VBM))
=>MQ_|_(VAB)
MQ=VB/2=3V2 cm ( MQ mediana in triunghiul VBM dreptunghic isoscel)
