To find the length of the larger rectangle, we can use the fact that similar rectangles have their corresponding sides in proportion.
The original rectangle has a length of 25 cm and a width of 12.25 cm. The larger rectangle has a width of 49 cm.
First, we find the scale factor between the width of the larger rectangle and the width of the original rectangle:
\[ \text{Scale Factor} = \frac{\text{Width of larger rectangle}}{\text{Width of original rectangle}} = \frac{49 \text{ cm}}{12.25 \text{ cm}}. \]
Calculating the scale factor:
\[ \text{Scale Factor} = \frac{49}{12.25} \approx 4. \]
Now we will use this scale factor to find the length of the larger rectangle:
\[ \text{Length of larger rectangle} = \text{Length of original rectangle} \times \text{Scale Factor} = 25 \text{ cm} \times 4 = 100 \text{ cm}. \]
Thus, the length of the larger rectangle is 100 cm.