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
4 cm 4 cm
24.01 cm 24.01 cm
98 cm
We can solve this problem by using the concept of similarity of shapes. The two rectangles are similar, which means that their corresponding sides are proportional.
Let's set up a proportion to find the length of the larger rectangle:
Length of larger rectangle / Length of smaller rectangle = Width of larger rectangle / Width of smaller rectangle
x / 25 = 49 / 12.25
Cross-multiplying, we have:
x * 12.25 = 25 * 49
x * 12.25 = 1225
Dividing both sides by 12.25, we get:
x = 1225 / 12.25
x ≈ 100
Therefore, the length of the larger rectangle is approximately 100 cm.