Question

A piece of wire 20 cm long is cut into two pieces , one of which is bent into a circle and the other into a square enclosing it. What is the length of the diameter of the circle?

Answer 1

Note that the diameter of the circle is equal to the length of the square and use that to set up an algebraic equation to find the diameter to be
`20/(pi+4)"cm" ~~ 2.8"cm"`

Explanation:

We'll proceed under the assumption that the square circumscribes the circle, and thus the diameter of the circle will be equal in length to a side of the square.

Let `d` equal the diameter of the circle. As the circumference of a circle is equal to `pid` and the perimeter of a square is four times the length of one of its sides, that is, `4d`. As the sum of the perimeters of the circle and the square add to the total length of the wire, we have

`pid + 4d = 20"cm"`

`=> d(pi+4) = 20"cm"`

`=> d = 20/(pi+4)"cm" ~~ 2.8"cm"`