Question

A rectangle has a length of 25 cm and a width of 12.25 cm. A larger, similar rectangle has width 49 cm. What is the length of the larger rectangle?(1 point)

98 cm 98 cm 24.01 cm 24.01 cm 100 cm 100 cm 4 cm

Answer 1

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**.