Question

The diagonal of the rectangle of maximum area having perimeter 100 cm is

• A. $10\sqrt{2}$
• B. $10$
• C. $25\sqrt{2}$
• D. $15$

Answer 1

Answer: (C)

$25\sqrt{2}$

$2(a+b)=100$
$d^2=a^2+b^2$
$d^2=a^2+(50-a{)}^2$
$2d\left(\frac{dd}{da}\right)=2a-2(50-a)$
$\frac{dd}{da}=0$ when $a=25$ $b=25$
$d=\sqrt{(25{)}^2+(25{)}^2}$
$d=25\sqrt{2}$