If the length of the diagonal of a square is 20 cm, then its perimeter must be :

A. $$10\sqrt 2 \,$$ cm

B. $$40 $$ cm

C. $$40\sqrt 2 \,$$ cm

D. $$ 200 $$ cm

Answer: Option C

Solution(By Examveda Team)

$$\eqalign{ & d = \sqrt 2 \times l \cr & \Rightarrow l = \frac{{20}}{{\sqrt 2 }} \cr} $$
∴ Perimeter :
$$\eqalign{ & = \left( {4l} \right)cm \cr & = \left( {\frac{{4 \times 20}}{{\sqrt 2 }} \times \frac{{\sqrt 2 }}{{\sqrt 2 }}} \right)cm \cr & = 40\sqrt 2 \,cm \cr} $$