Question
a rectangle has 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?
a. 24.01 cm
b. 100 cm
c. 98 cm
d. 4 cm
a. 24.01 cm
b. 100 cm
c. 98 cm
d. 4 cm
Answers
GPT-4o mini
To find the length of the larger rectangle, we can use the properties of similar rectangles. The ratio of the lengths will be the same as the ratio of the widths.
1. First, we find the ratio of the widths of the two rectangles:
\[
\text{Width ratio} = \frac{\text{Width of larger rectangle}}{\text{Width of smaller rectangle}} = \frac{49 \text{ cm}}{12.25 \text{ cm}}
\]
2. Now calculate this ratio:
\[
\text{Width ratio} = \frac{49}{12.25} \approx 4
\]
3. Next, we apply this ratio to the lengths of the rectangles. The length of the larger rectangle can be found by multiplying the length of the smaller rectangle by the same width ratio:
\[
\text{Length of larger rectangle} = \text{Length of smaller rectangle} \times \text{Width ratio}
\]
\[
\text{Length of larger rectangle} = 25 \text{ cm} \times 4 = 100 \text{ cm}
\]
Thus, the length of the larger rectangle is **100 cm**.
The correct answer is **b. 100 cm**.
1. First, we find the ratio of the widths of the two rectangles:
\[
\text{Width ratio} = \frac{\text{Width of larger rectangle}}{\text{Width of smaller rectangle}} = \frac{49 \text{ cm}}{12.25 \text{ cm}}
\]
2. Now calculate this ratio:
\[
\text{Width ratio} = \frac{49}{12.25} \approx 4
\]
3. Next, we apply this ratio to the lengths of the rectangles. The length of the larger rectangle can be found by multiplying the length of the smaller rectangle by the same width ratio:
\[
\text{Length of larger rectangle} = \text{Length of smaller rectangle} \times \text{Width ratio}
\]
\[
\text{Length of larger rectangle} = 25 \text{ cm} \times 4 = 100 \text{ cm}
\]
Thus, the length of the larger rectangle is **100 cm**.
The correct answer is **b. 100 cm**.