Question 280316
A square has twice the perimeter of a circle . the ratio of the area of the square to the area of the circle is 
A 4 b pi c 1/pi d 16/pi e none of these 

Let x be a side of the square.  The perimeter of the square is then 4*x. The perimeter (i.e. circumference) of the circle then is (1/2)*4x = 2x. The circumference is also given by pi*diameter = pi*2*r where r is the radius. 

So we have pi*2*r = 2*x and
r = 2x/2pi = x/pi

The area of the square is x*x = x^2
The area of the circle with radius r is pi*r^2

The ratios of the two areas is area of square/area of circle.

Using the fact that r = x/pi we the ratios become:

x^2/(pi*(x/pi)^2) =

x^2/(pi*(x^2/pi^2))=

(x^2/x^2)/(pi/pi^2)=
1/pi