12. Twelve congruent rectangles are placed together to make a rectangle $P Q R S$ as shown. What is the ratio $P Q: Q R$ ?
A $2: 3$
B $3: 4$
C 5:6
D $7: 8$
E $8: 9$
SOLUTION
$\mathbf{E}$

Let $l$ be the length of the long side, and $w$ be the length of the short side of each rectangle. Then $P S=3 l$ and $Q R=3 w+l$ so $2 l=3 w$ (since $P S=Q R$ ). Then $Q R=3 w+l=3 w+\frac{3}{2} w=\frac{9}{2} w$. Also, $P Q=2 l+w=4 w$. Hence the ratio $P Q: Q R$ is $4: \frac{9}{2}$, which is $8: 9$.