Dear forum members,

A problem asks me to show that a rectangle of constant area A has a minimal perimeter when the rectangle is a square.

I make the equation for the area and differentiate it with respect to x.

$\displaystyle P’(x)= 2-\frac{2A}{x^2}$

Solving for the zero points

$\displaystyle 2x^2-2A=0 $

At this stage, am I allowed to substitute A=xh into the equation and solve it as

$\displaystyle 2x^2-2xh=0$

$\displaystyle 2x(x-h)=0$

x=0 or x=h

or should I solve it as

$\displaystyle x=-\sqrt{A}$ or $\displaystyle x=\sqrt{A}$

because evidently the answer is different .

Please help me, I am really confused.

Thank you in advance.