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?
Since the rectangles are similar, their corresponding sides are proportional. The ratio of the length of the larger rectangle to the length of the smaller rectangle is equal to the ratio of the width of the larger rectangle to the width of the smaller rectangle.
Let the length of the larger rectangle be $l$. Since the width of the larger rectangle is 49 cm and the width of the smaller rectangle is 12.25 cm, we have that $\frac{l}{25}=\frac{49}{12.25}$. Cross multiplying gives $12.25l=49\cdot 25=1225$. Dividing both sides by 12.25, we find $l=\boxed{100}$ cm.