Question

`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?

Answer 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