Let angleBAC=x∠BAC=x
let AA be the area of DeltaABC A=1/2*AB*AC*sinx
we know that sinx has a maximum value of 1 ,
when sinx=1, A has the maximum value. => x=90^@
and given AB=AC=2011 cm angleABC=ACB=45^@ => BCsin45=AB => BC*1/sqrt2=2011 => BC=2011sqrt2 cm