2012 AMC 12B Problem 2

Attempt Problem 2 of the 2012 AMC 12B below, then check your answer against the professionally curated solution 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.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

$50$

$100$

$125$

$150$

$200$

Answer: E

Concepts:circle rectangle

Difficulty rating: 730

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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