2012 AMC 12B Problem 2

Problem 2 of 25EasierGeometry

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 circle is inscribed, so the width of the rectangle equals the diameter,

2\cdot5=10.

The length is then

2\cdot10=20,

so the area is

10\cdot20=200.

Thus, the correct answer is E.

Concepts: circle · rectangle

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