S=Area =c*k/2 As Hc=c is given, we need to maximize Ha*Hb : Ha=2*S/a Hb=2*S/b Denoting the angle between a and b as Gamma, we have the expression for the triangle area as : S=a*b*Sin(Gamma)/2 which leads to : a*b=2*S/Sin(Gamma) from the above: Ha*Hb=4*S^2/(a*b)=2*S*Sin(Gamma) The max. of Ha*Hb is therefore : 2*S=c*k and the max for Ha*Hb*Hc will be :