Answer: Option A
$$\eqalign{
& d = 4\sqrt 2 \,cm \cr
& \Rightarrow {\text{Area }} = \frac{1}{2}d_1^2 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2} \times {\left( {4\sqrt 2 } \right)^2} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 16}}\,{\text{c}}{{\text{m}}^2} \cr} $$
Area of new square = (2 × 16) cm2 = 32 cm2
$$\eqalign{
& \therefore \frac{1}{2}d_2^2 = 32 \cr
& \Rightarrow d_2^2 = 64 \cr
& \Rightarrow {d_2} = 8\,cm \cr} $$