2008 AMC 10A Problem 2

Attempt Problem 2 of the 2008 AMC 10A 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 2008 AMC 10A solutions, or check the answer key.

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

A square is drawn inside a rectangle. The ratio of the width of the rectangle to a side of the square is $2:1.$ The ratio of the rectangle's length to its width is $2:1.$ What percent of the rectangle's area is inside the square?

$12.5$

$25$

$50$

$75$

$87.5$

Answer: A

Concepts:area ratio percentage

Difficulty rating: 840

Solution:

Let the side of the square be $s,$ so its area is $s^2.$

The width of the rectangle is $2s,$ and its length is $2 \cdot 2s = 4s,$ giving an area of $8s^2.$

The fraction inside the square is $\dfrac{s^2}{8s^2} = \dfrac{1}{8} = 12.5\%.$

Thus, the correct answer is A.

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