AMC12 2012 B
AMC12 2012 B · Q2
AMC12 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?
如图，一个半径为 $5$ 的圆内接于一个矩形中。矩形的长与宽之比为 $2:1$。这个矩形的面积是多少？
(A)
50
50
(B)
100
100
(C)
125
125
(D)
150
150
(E)
200
200
Answer
Correct choice: (E)
正确答案：（E）
Solution
If the radius is $5$, then the width is $10$, hence the length is $20$. $10\times20= \boxed{\textbf{(E)}\ 200}.$
半径为 $5$，则宽为 $10$，因此长为 $20$。$10\times20= \boxed{\textbf{(E)}\ 200}.$
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