2011 AMC 10B Problem 3

Below is the professionally curated solution for Problem 3 of the 2011 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2011 AMC 10B solutions, or check the answer key.

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Concepts:area optimization

Difficulty rating: 770

At a store, when a length is reported as $x$ inches that means it is at least $x - 0.5$ inches and at most $x + 0.5$ inches. Suppose the dimensions of a rectangular tile are reported as $2$ inches by $3$ inches. In square inches, what is the minimum area for the rectangle?

$3.75$

$4.5$

$5$

$6$

$8.75$

Solution:

The smallest possible dimensions are $1.5\times 2.5,$ so the area is $1.5\cdot 2.5=3.75.$

Thus, the correct answer is A .

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