2020 AMC 12A Problem 16

A point is chosen at random within the square in the coordinate plane whose vertices are (0, 0), (2020, 0), (2020, 2020), and (0, 2020). The probability that the point is within d units of a lattice point is \tfrac{1}{2}. (A point (x, y) is a lattice point if x and y are both integers.) What is d to the nearest tenth?

\textbf{(A) } 0.3 \qquad \textbf{(B) } 0.4 \qquad \textbf{(C) } 0.5 \qquad \textbf{(D) } 0.6 \qquad \textbf{(E) } 0.7

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.