To find the length of the larger, similar rectangle, we can use the property of similar figures, which states that the ratio of corresponding sides is constant.
Given:
- Length of the smaller rectangle (L1) = 25 cm
- Width of the smaller rectangle (W1) = 12.25 cm
- Width of the larger rectangle (W2) = 49 cm
First, we calculate the ratio of the widths:
\[ \text{Ratio} = \frac{W2}{W1} = \frac{49 , \text{cm}}{12.25 , \text{cm}} \]
Now, calculate that ratio:
\[ \text{Ratio} = \frac{49}{12.25} \approx 4 \]
Now, we use this ratio to find the length of the larger rectangle (L2):
\[ L2 = L1 \times \text{Ratio} = 25 , \text{cm} \times 4 = 100 , \text{cm} \]
Thus, the length of the larger rectangle is 100 cm.