In the figure, `deltaabc` is congruent to `deltaadc`. if the square abcd is dilated by a factor of 2 to form a'b'c'd', what is the ratio of the area of a'b'c'd' to the area of abcd? 2: 1 3: 1 4: 1 5: 1

The square is dilated by a factor of 2 to form A'B'C'D'.

Which mean the new square sides will be twice as much as the old square.

Let the side length of the square ABCD = x

∴ The side length of the square A'B'C'D' =2x

∵ The area of the square = (side length)²

Area of ABCD = x²

Area of A'B'C'D'= (2x)² = 4x²

∴ Area of A'B'C'D' :  Area of ABCD = 4x² : x² = 4 : 1