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
4 cm
4 cm
100 cm
To find the length of the larger rectangle, we can use the concept of similarity.
Two rectangles are similar if their corresponding sides are proportional. In this case, we know that the length of the first rectangle is 25 cm and the width is 12.25 cm.
If we compare the lengths of the two rectangles, we can set up the proportion:
Length of larger rectangle / Length of smaller rectangle = Width of larger rectangle / Width of smaller rectangle.
Let "x" represent the length of the larger rectangle.
x / 25 = 49 / 12.25
Cross-multiplying, we get:
12.25x = 1225
Dividing both sides by 12.25, we find:
x = 100 cm
Therefore, the length of the larger rectangle is 100 cm.