Christmas party with rabbits

Geometry Level 4

A rabbit lives on a triangular piece of land which is in the shape of an isosceles right triangle, with vertices \( (0,0), (0, n), (n,0) \).

On Christmas day, he organizes a party for his friends, and wanted to dress up in a Santa suit, stand at the origin and throw gifts at them. He wanted each of his friends to stand at a point within the island (not on the border) that has integral coordinates. He found that he can invite a maximum of 210 of his friends.

Using the information above, find the area of his land in unit squares.

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