A square has a diagonal measuring 4√2 cm. If another square has an area twice as large as the first square, what is the length of the diagonal of this second square?

Explanation

First, calculate the area of the original square using the formula: Area = ½ × (diagonal)² = ½ × (4√2)² = ½ × 32 = 16 cm². The second square's area is twice that, so 2 × 16 = 32 cm². Let the diagonal of the second square be D cm. Using the same formula: ½ × D² = 32, which gives D² = 64, and therefore D = 8 cm.