A wire of length $\text{36m}$ is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle, and the circumference of the circle is $\text{k}$ (meter), then $\left(\frac{4}{\pi }+1\right)k$  is equal to ___

Let  $x$ be perimeter of square and $y$  be perimeter of circle side of square
$\therefore x+y=36$ 
Side of the square = $\frac{x}{4}$  and radius of the circle = $\frac{y}{2\pi }$ 
$\therefore$  Sum of areas,  $f\left(x\right)={\left(\frac{x}{4}\right)}^2+\pi {\left(\frac{y}{2\pi }\right)}^2=\frac{x^2}{16}+\frac{{\left(36-x\right)}^2}{4\pi }$
$f\text{'}\left(x\right)=\frac{2x}{16}-\frac{2\left(36-x\right)}{4\pi }=0$ 
$\therefore x=\frac{144}{\pi +4}$$\Rightarrow \left(\frac{4}{\pi }+1\right)k=36$