The diagonal of a square A is (a+b). The diagonal of a square whose area is twice the area of square A is:

\(\sqrt {2}\)(a+b)

Diagonal of a square = \(\sqrt {2}\) × s                 [s = side]

                   \(\sqrt {2}\) side = a + b

                          side  = \(\frac{a + b}{\sqrt {2}}\)

⇒ Area of 1st square = \((\frac{a + b}{\sqrt {2}})^{2}\)

⇒ Area of 2nd square = 2 × \((\frac{a + b}{\sqrt {2}})^{2}\) = (a + b)²

⇒ Area of 2nd square = (side)² = (a + b)²

⇒ Side of the 2nd square = a + b

⇒ Diagonal = \(\sqrt {2}\) (a + b)