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

Answer: Option C

$$\begin{array}{rl}& d=\sqrt{2}\times l\\ & \Rightarrow l=\frac{20}{\sqrt{2}}\end{array}$$
∴ Perimeter :
$$\begin{array}{rl}& =\left(4l\right)cm\\ & =\left(\frac{4\times 20}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}\right)cm\\ & =40\sqrt{2}cm\end{array}$$