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)
Responses

24.01 cm
24.01 cm

100 cm
100 cm

98 cm
98 cm

4 cm

Answer 1

To find the length of the larger rectangle, we first need to determine the scaling factor between the two rectangles. Since the rectangles are similar, the ratio of their corresponding sides will be the same.

The original rectangle has:
- Length = 25 cm
- Width = 12.25 cm

The width of the larger rectangle is given as 49 cm. We can calculate the scale factor based on the widths:

\[
\text{Scale Factor} = \frac{\text{Width of larger rectangle}}{\text{Width of smaller rectangle}} = \frac{49}{12.25}
\]

Calculating this:

\[
\frac{49}{12.25} \approx 4
\]

Now, we apply the same scale factor to find the length of the larger rectangle:

\[
\text{Length of larger rectangle} = \text{Length of smaller rectangle} \times \text{Scale Factor} = 25 \times 4 = 100 \text{ cm}
\]

Thus, the length of the larger rectangle is **100 cm**.

So, the correct response is:

**100 cm**