Question 507047
Suppose the area of a circle is numerically equal to the perimeter of a square and that the length of a radius of the circle is equal to the length of a side of the square.
 Find the length of a side of the square. Express answer in terms of pi
:
let s = side of the square
then
4s = the perimeter of the square
:
It says,"the area of a circle is numerically equal to the perimeter of a square" therefore
{{{pi*r^2}}} = 4s
and
"the length of a radius of the circle is equal to the length of a side of the square." therefore:
r = s
:
In the 1st equation, replace r with s
{{{pi*s^2}}} = 4s
divide both sides by s
{{{pi*s}}} = 4
divide both sides by pi
s = {{{4/pi}}}