SOLUTION: A piece of wire 30com long is cut into two pieces. One of these is bent into a circle and the other is bent into a square enclosing the circle. What is the diameter of the circle?

Question 204772This question is from textbook Longman Mathematics
: A piece of wire 30com long is cut into two pieces. One of these is bent into a circle and the other is bent into a square enclosing the circle. What is the diameter of the circle? This question is from textbook Longman Mathematics

Found 2 solutions by ankor@dixie-net.com, jsmallt9:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A piece of wire 30com long is cut into two pieces.
One of these is bent into a circle and the other is bent into a square enclosing the circle.
What is the diameter of the circle?
;
The diameter of the circle is also the side of the square
:
Let x = the diameter and the side of the square
;
Circum + perimeter = 30
pi*x + 4x = 30
;
4.71416x = 30
x =
x = 4.2 cm is the diameter of the circle
:
:
Check
circum: 4.2*pi = 13.195
perime: 4 * 4.2= 16.80
------------------------
wire length = 29.995 ~ 30
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
In another solution to this problem there are some errors (which are probably typing errors). So I am going to provide a correct solution, based on the otherwise correct solution.

The diameter of the circle is also the side of the square
:
Circumference (C) + perimeter of the square (P) = 30

;
Let x = the diameter and the side of the square
;
Substituting these into the equations

Using the approximation we get

approximately.

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