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

98 cm
98 cm

100 cm
100 cm

4 cm

Answer 1

To find the length of the larger rectangle, we can use the fact that similar rectangles have their corresponding sides in proportion.

The original rectangle has a length of 25 cm and a width of 12.25 cm. The larger rectangle has a width of 49 cm.

First, we find the scale factor between the width of the larger rectangle and the width of the original rectangle:

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

Calculating the scale factor:

\[
\text{Scale Factor} = \frac{49}{12.25} \approx 4.
\]

Now we will use this scale factor to find the length of the larger rectangle:

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

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