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)
To find the length of the larger rectangle, we can set up a proportion comparing the lengths and widths of the two rectangles.
The proportion will be:
l1 / w1 = l2 / w2
where l1 is the length of the smaller rectangle, w1 is the width of the smaller rectangle, l2 is the length of the larger rectangle, and w2 is the width of the larger rectangle.
Substituting the given values, we have:
25 cm / 12.25 cm = l2 / 49 cm
We can solve this proportion by cross-multiplying:
25 cm * 49 cm = 12.25 cm * l2
1225 cm^2 = 12.25 cm * l2
Now we can solve for l2 by dividing both sides of the equation by 12.25 cm:
l2 = 1225 cm^2 / 12.25 cm
l2 = 100 cm
Therefore, the length of the larger rectangle is 100 cm.