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

Answer 1

To find the length of the larger rectangle that is similar to the smaller rectangle, we can use the concept of proportionality.

First, we find the ratio of the widths of the large rectangle to the small rectangle:
- Width of the smaller rectangle = 12.25 cm
- Width of the larger rectangle = 49 cm

The ratio of the widths is:
\[
\text{Ratio} = \frac{\text{Width of larger rectangle}}{\text{Width of smaller rectangle}} = \frac{49}{12.25}
\]

Next, we simplify that ratio:
\[
\frac{49}{12.25} = 4
\]

This means that the larger rectangle is 4 times wider than the smaller rectangle.

Since the rectangles are similar, their lengths will also be in the same proportion:
\[
\text{Length of larger rectangle} = \text{Length of smaller rectangle} \times \text{Ratio}
\]
\[
\text{Length of larger rectangle} = 25 \text{ cm} \times 4 = 100 \text{ cm}
\]

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