Let the radius of the circle and the semicircle by r.

Let ABCD be the square inscribed in the semicircle.

OB² = OC² + BC²

r² = + x²

r² = x²

\ The area of the square = x² = r^2.

Diagonal of the square = 2r = side = 2r.

Side of the square EFGH = r.

Area of the square = 2r².

The ratio of the area of the square ABCD to the area of the square EFGH = r² : 2r²

= 2 : 5 Choice (3)