Alcivious draws a square with a side that measures 5 cm. He dilates the square using a scale factor of 4. What is the ratio of the area of the dilated square to the area of the original square? Use a decimal response if necessary.

Answer 1

The area of the original square is equal to the side length squared, so it is $5\text{ cm} \times 5\text{ cm} = 25\text{ cm}^2$. The scale factor of 4 means each side length of the dilated square is multiplied by 4, so the side length of the dilated square is $5\text{ cm} \times 4 = 20\text{ cm}$. The area of the dilated square is therefore $20\text{ cm} \times 20\text{ cm} = 400\text{ cm}^2$. The ratio of the area of the dilated square to the area of the original square is then $\frac{400\text{ cm}^2}{25\text{ cm}^2} = \boxed{16}$.