To solve the problem, we first find the area of the original square and the area of the dilated square.
-
Calculate the area of the original square: The side length of the square is 10 units. The area \( A \) of a square is given by the formula: \[ A = \text{side}^2 \] Therefore, the area of the original square is: \[ A_{\text{original}} = 10^2 = 100 \text{ square units} \]
-
Apply the dilation with the scale factor \( \frac{25}{25} \) (which simplifies to 1): Since the scale factor is \( \frac{25}{25} = 1 \), the new side length of the dilated square, \( s' \), is: \[ s' = s \times \text{scale factor} = 10 \times 1 = 10 \text{ units} \]
-
Calculate the area of the dilated square: The area of the dilated square is: \[ A_{\text{dilated}} = (s')^2 = 10^2 = 100 \text{ square units} \]
-
Write the area of the dilated square as a fraction of the area of the original square: \[ \frac{A_{\text{dilated}}}{A_{\text{original}}} = \frac{100}{100} = 1 \]
Since 1 can be written as a fraction, the lowest terms would be \( \frac{1}{1} \) or simply \( 1 \).
So, the correct response is: \[ 1 \]