A square is inscribed in a right triangle, as shown below. The legs of the triangle are 2 and 3. Find the side length of the square.
Here is the code:
[asy]
unitsize(1.5 cm);
pair A, B, C, D, E, F, G;
A = (0,0);
C = (5,0);
B = (3^2/5,3*4/5);
D = extension(B, A + (0,-5), A, C);
G = extension(B, C + (0,-5), A, C);
E = extension(D, D + (0,1), A, B);
F = extension(G, G + (0,1), B, C);
draw(A--B--C--cycle);
draw(D--E--F--G);
[/asy]
