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2012 AMC 10B Problem 2

Problem 2 of 25EasierGeometryArithmetic

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 smaller side of the rectangle is equal to the diameter, which is 2r=2⋅5=10.2r=2\cdot 5=10. Due to the 2:12:1 ratio, the long side is 10⋅2=20.10\cdot 2=20. Therefore, the area is 20⋅10=200.20\cdot 10=200. Thus, the correct answer is E .
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Tagged: circle · rectangle · ratio and proportion

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