A square has an area of $25.$ A rectangle has the same width as the square. The length of the rectangle is double its width. What is the area of the rectangle?
For the square to have an area of $25,$ each side length must be $\sqrt{25}=5.$

The rectangle's width is equal to that of the square and therefore must also be $5.$ The length of the rectangle is double its width or $5\times 2=10.$ The area of the rectangle is thus $5\times 10=\boxed{50}.$