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

Answer 1

To find the length of the larger rectangle, we can use the properties of similar rectangles, which maintain the same proportional dimensions.

1. First, find the ratio of the widths of the smaller rectangle to the larger rectangle: \[ \text{Ratio} = \frac{\text{Width of smaller rectangle}}{\text{Width of larger rectangle}} = \frac{12.25 \text{ cm}}{49 \text{ cm}} \]

2. Next, since the rectangles are similar, this ratio applies to the lengths as well. Thus: \[ \frac{\text{Length of smaller rectangle}}{\text{Length of larger rectangle}} = \frac{25 \text{ cm}}{\text{Length of larger rectangle}} \]

3. We can set up our equation using the ratios: \[ \frac{12.25}{49} = \frac{25}{\text{Length of larger rectangle}} \]

4. Cross multiply to solve for the length of the larger rectangle: \[ 12.25 \cdot \text{Length of larger rectangle} = 25 \cdot 49 \]

   \[ 12.25 \cdot \text{Length of larger rectangle} = 1225 \]

5. Now, divide both sides by 12.25: \[ \text{Length of larger rectangle} = \frac{1225}{12.25} = 100 \text{ cm} \]

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