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. \(4\sqrt{2}\) cm
• D. 16 cm

Hint:

Diagonal squared is proportional to area for a square, so doubling the area means the diagonal scales by root 2.

Answer 1

The Correct Option is A

Step 1: Find the side of the first square.
For a square of side \(a\), the diagonal is \(a\sqrt{2}\). Here the diagonal is \(4\sqrt{2}\), so \(a\sqrt{2} = 4\sqrt{2}\), which gives \(a = 4\) cm.

Step 2: Find the area of the first square, then the second.
Area of the first square \( = a^2 = 4^2 = 16\) sq cm. The second square has double this area, so its area \( = 2 \times 16 = 32\) sq cm.

Step 3: Find the side and then the diagonal of the second square.
Side of the second square \( = \sqrt{32} = 4\sqrt{2}\) cm. Its diagonal \( = \text{side} \times \sqrt{2} = 4\sqrt{2} \times \sqrt{2} = 4 \times 2 = 8\) cm.

Final Answer:
The diagonal of the second square works out to 8 cm, so option A is correct, while B, C and D do not match this value. \[ \boxed{8 \text{ cm}} \]