Correct Answer – Option 3 : 8 cm

Given:

The length of the diagonal of the square is 4√2 cm

Concept Used:

If the length of one side of a square is ‘a’ unit then the length of diagonal of the square is a√2 unit.

And the arear of the square is a² square unit.

Calculation:

Let, the length of one side of the square is ‘a’ unit

⇒ Length of the diagonal of the square is a√2 unit

Accordingly,

a√2 = 4√2

⇒ a = 4

Area of the square is 4² = 16 cm²

Accordingly, the area of the 2nd square is 2 × 16 = 32 cm²

Let, the length of the side of the 2nd square is ‘b’

Accordingly, 

b² = 32

⇒ b = √32

⇒ b = 4√2

Length of the diagonal of the 2nd square is (4√2) × √2

⇒ 8 cm

∴ The diagonal of another square whose area is double that of the first square is 8 cm.