BdMO Online Forum

Siam wants to build a new garden.He wants to make a garden with perimeter $P$ and area $A$ and he also wants to keep the value of $\dfrac{ P^2}{A}$ as small as he can. What will be the lowest value of $\dfrac{P^2}{A}$?

If the garden is square shaped then , $\dfrac{P^2}{A}=16 $
But if it is a circle shaped grden then,
$\dfrac{P^2}{A}=4\pi$
As,$4\pi<16 $

The desired answer is $4\pi$