1998 AHSME Problem 29

Geometry Level 3

A point (x,y) in the plane is called a lattice point if both x and y are integers. The area of the largest square that contains exactly three lattice points in its interior is closest to

4 4.5 5.6 4.2

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1 solution

Applying Pick's Theorem,

A = I + (B/2) - 1,

where A is the area, I is the number of points in the interior, and B is the number of points on the boundary

A = 3 + (4/2) - 1 = 4.

How do you know that the vertices must be on lattice points? If they do not, why does Pick's theorem apply?

Mark Kong - 7 years ago

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Thanks, I've updated the answer.

Calvin Lin Staff - 7 years ago

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WHEN I ANSWERED 4 IT TOLD ME WRONG!!!

Parth Lohomi - 6 years, 10 months ago

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