A square and a circle have equal perimeters. What is the ratio of the area of the circle to the area of the square? (Use π = 22/7.)

Let the common perimeter be $P$. The square's side is $P/4$, so its area is $P^2/16$. For the circle, 2π$r=P$ gives $r=P/2$π and area π$r^2=P^2/4$π. The ratio circle : square = $(P^2/4$π) : $(P^2/16)=16$ : 4π = 4 : π = 4 : 22/7 = 28 : 22 = 14 : 11. The trap 1 : 1 assumes equal perimeters force equal areas; 11 : 14 reverses the order and makes the circle the smaller, though for a fixed perimeter the circle is always the larger; 22 : 7 quotes π itself.