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

A. 9 cm

B. 18 cm

C. 20 cm

D. 41 cm

Answer: Option B

Solution(By Examveda Team)

$$\eqalign{ & \sqrt {{l^2} + {b^2}} = \sqrt {41} \cr & \Rightarrow {l^2} + {b^2} = 41 \cr & Also,\,\,lb = 20 \cr & {\left( {l + b} \right)^2} = \left( {{l^2} + {b^2}} \right) + 2lb \cr & {\left( {l + b} \right)^2} = 41 + 40 \cr & {\left( {l + b} \right)^2} = 81 \cr & \left( {l + b} \right) = 9 \cr & \therefore {\text{ Perimeter}} = 2\left( {l + b} \right) = 18\,cm \cr} $$