2011 AMC 10B Problem 3

Question

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

Use the smallest possible length and width

The reported

2

by

3

tile can be as small as

1.5

by

2.5

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 .

Problem 3 in other years