Australian AMC 2015 - Intermediate Question 15

Question 15

The diagram shows part of a tiled floor. The tiles are all squares, of seven different sizes. The smallest tile is $1\text{ cm}\times1\text{ cm}$ and the next smallest is $3\text{ cm}\times3\text{ cm}$.

What is the distance $XY$?

Question illustration

$\sqrt{346}\text{ cm}$
19 cm
$\sqrt{369}\text{ cm}$
$\sqrt{377}\text{ cm}$
20 cm