2012 AMC 10B Problem 2

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?

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Solution

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 .

Concepts: circle · rectangle · ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.