Question

如图，一个半径为 $5$ 的圆内切于一个长方形。长方形的长与宽之比为 $2:1$ 。长方形的面积是多少？

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?

$50$

$100$

$125$

$150$

$200$

答案：E

知识点：圆矩形比与比例

难度评级：560

解答：

短边等于圆的直径，即 $2r=2\cdot 5=10$ 。

长与宽之比为 $2:1$ ，所以长边为 $10\cdot 2=20$ 。

长方形面积为 $20\cdot 10=200$ 。

所以正确答案是 E。

The smaller side of the rectangle is equal to the diameter, which is $2r=2\cdot 5=10.$

Due to the $2:1$ ratio, the long side is $10\cdot 2=20.$

Therefore, the area is $20\cdot 10=200.$

Thus, the correct answer is E .

2012 AMC 10B 第 2 题

答案：E

难度评级：560

解答：

其他年份的第 2 题