11.4 a) A rectangle with an area of 2018 is placed on the coordinate plane such that its sides are parallel to the coordinate axes, and all four vertices lie within different quadrants and have integer coordinates. Find the length of its diagonal. b) Does there exist a rectangle with an area of 2018 and integer vertices within different quadrants, where the sides are not parallel to the coordinate axes?
Answer. a) $\sqrt{1018085} ;$ b) exists. Solution. See problem 10.4.

## 1st round. 11.11.2018

## 11th grade