To find the length of the larger rectangle that is similar to the smaller rectangle, we can use the property of similar rectangles, which states that the ratios of their corresponding dimensions are equal.
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
Let L2 be the length of the larger rectangle. The ratio of the widths should equal the ratio of the lengths:
\[ \frac{L1}{W1} = \frac{L2}{W2} \]
Substituting the known values:
\[ \frac{25}{12.25} = \frac{L2}{49} \]
Now we can solve for L2:
\[ \frac{25}{12.25} = \frac{L2}{49} \]
Cross-multiplying gives:
\[ 25 \cdot 49 = 12.25 \cdot L2 \]
Calculating the left side:
\[ 1225 = 12.25 \cdot L2 \]
Now, divide both sides by 12.25 to find L2:
\[ L2 = \frac{1225}{12.25} \]
Calculating this gives:
\[ L2 = 100 \]
Thus, the length of the larger rectangle is 100 cm.
The correct response is: 100 cm.