problem: The points $(1,-2)$ and $(-4,10)$ are adjacent vertices of a square. What is the perimeter of the square?
solution: The side length of the square is the distance between the given points, or $\sqrt{(1 - (-4))^2 + ((-2) - 10)^2} = \sqrt{5^2 + 12^2} = 13$. The perimeter of the square is four times the side length, or $4 \times 13 = \boxed{52}$.