∵DE⊥AC,BC⊥AC，

∴△ADE∽△ABC，

∴AEAC=DEBC,2？ x2=x2，

The solution is x= 1,

∴S square =1;

As shown in figure b:

The side length of an isosceles right triangle is 2,

∴AB=AC2+BC2=22+22=22，

Let the side length of a square be x, then AD=22? x2=2-x2，

∠∠A =∠A，∠ADE=∠ACB，

∴△ADE∽△ACB，

∴ADAC=DEBC,2？ x22=x2，

The solution is x=223.

∴S square = (223) 2 = 89;

∵ 1>89,

∴ A-type cutting method has a large area;

(2) Yes.

As shown in figure c:

Let the side length of a square be x, then AE=3-x,

∵DE⊥AC,BC⊥AC，

∴△ADE∽△ABC，

∴AEAC=DEBC,3？ x3=x4，

x = 127≈ 1.7 1 > 1.7，

Cut out a square with a side length of 1.7.