2012 AMC 12B 第 2 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
2.
如图，一个半径为 的圆内切于一个长方形。长方形的长与宽之比为 。这个长方形的面积是多少？
A circle of radius is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is What is the area of the rectangle?
小提示：
长方形的宽等于圆的直径
The width of the rectangle equals the diameter of the circle
大提示：
长方形的长是宽的两倍
The length is twice the width
解答：
圆内切于长方形，所以长方形的宽等于圆的直径，即 。
长方形的长为 ，所以面积为 。
因此正确答案是 E。
The circle is inscribed, so the width of the rectangle equals the diameter,
The length is then so the area is
Thus, the correct answer is E.
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