2012 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2012 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 12B solutions, or check the answer key.

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Concepts:circle rectangle

Difficulty rating: 730

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?

$50$

$100$

$125$

$150$

$200$

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.

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