∵CDEF is rectangular, and f is on BC.

∴DE∥CB

∴△ADE∽△ACB

∴AD/AC = Germany/CB ...

∠∠A = 30，∠C=90，AB= 12

∴AC=6√3,BC=6.......②

Let DC = X.

Then ad = 6 √ 3-x...③

Synthesizing ① ② ③, DE = 6-(√ 3/3) X is obtained.

∴scdef=dc×de=x[6-(√3/3)x]=-(√3/3)x？ + 6x=-(√3/3)(x？ - 6√3x)=(-√3/3)(x - 3√3)？ + 9√3

When x=3√3, the maximum value of rectangular CDEF is 9√3.

∫AC = 6√3，DC=3√3

∴D is the midpoint of AC

∫DE∫CB

∴E is the midpoint of AB