2011 AMC 10B Problem 3

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?

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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 .

Concepts: area · optimization

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.