The diagonal of a square measures $6\sqrt{2}$cm. The measure of the diagonal of a square whose area is twice that of the first square is:

12 cm

We know that,

Diagonal of square = \(\sqrt {2}\) × Side of square

We have,

The diagonal of the square =  6\(\sqrt {2}\) cm

So, \(\sqrt {2}\) × Side of square = 6\(\sqrt {2}\)

Side of square = 6 cm

Area of first square = 6 × 6 = 36 cm²

Area of second square = 2 × 36 = 72 cm²

The side of the second square = \(\sqrt {72}\) = 6\(\sqrt {2}\)

The diagonal of second square =  \(\sqrt {2 × area of square }\) = \(\sqrt {2 × 72 }\) = \(\sqrt {144}\) = 12