Question

What is the largest possible area for a rectangle with a perimeter of 40 cm?

Answer 1

$p=2(a+b)=40\\S=ab=a(p/2-a)=ap/2-a^2\\S'=p/2-2a=0\quad\Rightarrow\quad a=p/4=10,b=p/2-a=p/4=10\\S_{\max}=100$