Question 459960
A wire 41 inches long needs to be cut into three pieces so that it can be formed into two identical circles and a square. 
The length of the side of the square must equal the diameter of the circles.
approximate where the wire should be cut.
:
Let x = the side of the square and the diameter of the circles
:
4x = the perimeter of the square
:
{{{pi*x) = circumference of the circle
then
{{{2*pi*x)}}} = circumference of two circles
:
perimeter of the square + the circumference of two circles = 41
4x + {{{2*pi*x}}} = 41
Find x
4x + 6.2832x = 41
10.2832x = 41
x = {{{41/10.23832}}}
x = 3.9871 ~ 4 inches the side of the square and the diameter of the circles
:
Cut 4(4) = 16 inches, leaving 41 - 16 = 25 inches remain
Cut the remainder in half, each = 12.5 inches, circumference of each circle
:
Check this by finding the circumference using x=4
{{{pi*4}}} = 12.6 inches, close enough to 12.5, don't you agree?