AMC10 2012 B

AMC10 2012 B · Q2

AMC10 2012 B · Q2. It mainly tests Circle theorems, Area & perimeter.

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?

一个半径为 5 的圆内切于一个矩形中，如图所示。矩形的长宽比为 2 : 1。矩形的面积是多少？

(A) 50 50

(B) 100 100

(D) 150 150

(E) 200 200

Answer

Correct choice: (E)

正确答案：（E）

Solution

The width of the rectangle is the diameter of the circle, so the\nwidth is $2 \cdot 5 = 10$. The length of the rectangle is $2 \cdot 10 = 20$. Therefore the area\nof the rectangle is $10 \cdot 20 = 200$.

矩形的宽度是圆的直径，因此宽度为 $2 \cdot 5 = 10$。矩形的长度为 $2 \cdot 10 = 20$。因此矩形的面积为 $10 \cdot 20 = 200$。

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