Question

The diagonal of a square is \(4\sqrt{2}\) cm. The diagonal of another square whose area is double that of the first square is

• A. 8 cm
• B. \(8\sqrt{2}\) cm
• C. \(4\sqrt{3}\) cm
• D. 16 cm

Answer 1

The Correct Option is A

Given: The diagonal of the first square is \(4\sqrt{2}\) cm.

Method 1 — Using side and area:
Side of first square \(s_1 = \dfrac{\text{diagonal}}{\sqrt{2}} = \dfrac{4\sqrt{2}}{\sqrt{2}} = 4\) cm.
Area of first square \(A_1 = s_1^2 = 4^2 = 16\ \text{cm}^2\).
Area of second square \(A_2 = 2A_1 = 2 \times 16 = 32\ \text{cm}^2\).
Side of second square \(s_2 = \sqrt{A_2} = \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2}\ \text{cm}\).
Diagonal of second square \(d_2 = s_2 \sqrt{2} = (4\sqrt{2})\sqrt{2} = 4 \times 2 = 8\ \text{cm}\).

Method 2 — Using scale factor for area:
If area doubles, linear dimensions (side, diagonal) scale by \(\sqrt{2}\).
Hence \(d_2 = d_1 \times \sqrt{2} = (4\sqrt{2}) \times \sqrt{2} = 4 \times 2 = 8\ \text{cm}\).

Final Answer: 8 cm (Option A).