2012 AMC 10B 第 2 题

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

长方形的宽等于圆的直径。

The rectangle width is the circle diameter

求出宽后，用长宽比

2:1

求长。

Use the

2:1

length-to-width ratio after finding the width

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 .

其他年份的第 2 题