The diagonal of a square is 4 2 cm. The diagonal of another square whose area is double that of the first square, is :

Answer: Option A

$$\begin{array}{rl}& d=4\sqrt{2}cm\\ & \Rightarrow \text{Area }=\frac{1}{2}{d}_1^2\\ & =\frac{1}{2}\times {\left(4\sqrt{2}\right)}^2\\ & \text{ = 16}\text{c}{\text{m}}^2\end{array}$$
Area of new square = (2 × 16) cm² = 32 cm²
$$\begin{array}{rl}& \therefore \frac{1}{2}{d}_2^2=32\\ & \Rightarrow d_2^2=64\\ & \Rightarrow d_2=8cm\end{array}$$