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2012 AMC 12B Problem 2

Problem 2 of 25EasierGeometry

A circle of radius 55 is inscribed in a rectangle as shown. The ratio of the length of the rectangle to its width is 2:1.2:1. 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⋅5=10.2\cdot5=10. The length is then 2⋅10=20,2\cdot10=20, so the area is 10⋅20=200.10\cdot20=200. Thus, the correct answer is E.
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