Question

The diagonal of a rectangle is $\sqrt{41}$ cm and its area is 20 sq cm The perimeter of the rectangle must be:

• A. $9cm$
• B. $18cm$
• C. $41cm$
• D. $20cm$

Answer 1

The correct option is B $18cm$

From the figure we have,

$l^2+b^2={\left(\sqrt{41}\right)}^2=41.$

Also $lb=20$
We know that,
$(l+b{)}^2=l^2+b^2+2lb$
$=41+2\times 20=41+40=81$
$\Rightarrow l+b=\sqrt{81}=9$
$\therefore$ Perimeter $=2(l+b)=2\times 9=18cm$