19. The diagram shows two overlapping rectangles, each measuring $p$ by $q$. The area of overlap is exactly one-quarter of the total area of the figure.
What is the ratio $p: q$ ?
A $5: 2$
B $4: 1$
C 3:1
D $2: 1$
E $3: 2$
19. A The area of each rectangle is $p q$ and the area of overlap is $q^{2}$, so the total area of the figure is $2 p q-q^{2}$. Therefore $q^{2}=\frac{1}{4}\left(2 p q-q^{2}\right)$. Hence $4 q^{2}=2 p q-q^{2}$. So $5 q^{2}=2 p q$.
Now $q \neq 0$, so $5 q=2 p$. Therefore $p: q=5: 2$.