Question

If all the rectangles of a given perimeter $2P$, the one having the smallest diagonal is square whose side is?

• A. $\frac{P}{2}$
• B. $P$
• C. $2P$
• D. $\frac{P}{3}$

Answer 1

The correct option is A $\frac{P}{2}$

Let a and b be the length and breadth of rectange respectively

$2(a+b)=2p$
$d^2=a^2+b^2$
$d=\sqrt{a^2+(p-a{)}^2}$
$\frac{d\left(d\right)}{d\left(a\right)}=\frac{1(2a-2(p-a\left)\right)}{2\sqrt{a^2+(2p-a{)}^2}}$
$0=4a-2p$
$\frac{P}{2}=a$.