2012 AMC 10B Problems/Problem 2
A circle of radius 5 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1. What is the area of the rectangle?
Note that the diameter of the circle is equal to the shorter side of the rectangle. Since the radius is , the diameter is . Since the sides of the rectangle are in a ratio, the longer side has length . Therefore the area is or .