A wire of length 28m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the lengths of the two pieces so that the combined area of the circle and the square is minimum?

Explanation

Let one part be `x`, then the other part is `28−x.`

Assume that the part of length `x` is converted into a circle of radius `r`.

`2pir=x`

`implies r=2pix`

Area of circle ` =pir^2`

`=pi(x/{2pi})^2`

`={x^2}/{4pi}`

Now second part of length `28−x` is converted into a square.

...