length = [tex]l[/tex]
width = w = [tex]\frac{2}{3}\cdotl[/tex]
[tex]l\cdot\frac{2}{3}l = 864[/tex]
[tex]\frac{2}{3}l^2 = 864[/tex]
[tex]l^2 = 864\cdot\frac{3}{2}[/tex]
[tex]l^2 = 1296[/tex]
[tex]\boxed{l=36}[/tex]
[tex]w=\frac{2}{3}\cdot36[/tex]
[tex]\boxed{w=24}[/tex]