IKMC 2010 - Grades 11-12 - Paper 01 - Self-study Question 25

Question 25

A wall is tiled with two sizes of square tiles, of side lengths $a$ and $b$, with $a>b$. The horizontal and sloping dashed lines in the pattern form a $30^\circ$ angle. Find $a:b$.

Question illustration

$(2\sqrt3):1$
$(2+\sqrt3):1$
$(3+\sqrt2):1$
$(3\sqrt2):1$
$2:1$