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

There is a faster route here that skips finding the side length at all, since for any square the area is proportional to the square of its diagonal: area $= \dfrac{d^2}{2}$, where $d$ is the diagonal.

1. Write the area of the first square in terms of its diagonal: $A_1 = \dfrac{d_1^2}{2} = \dfrac{(4\sqrt{2})^2}{2} = \dfrac{32}{2} = 16$ sq cm, matching the side-based method.
2. The second square has area $A_2 = 2A_1 = 32$ sq cm.
3. Using the same formula in reverse, $d_2^2 = 2A_2 = 2 \times 32 = 64$, so $d_2 = \sqrt{64} = 8$ cm.

Since area scales with the square of the diagonal, doubling the area means the diagonal scales by $\sqrt{2}$, so $d_2 = 4\sqrt{2} \times \sqrt{2} = 8$ cm, which confirms the same result without ever computing the side length.

Let's summarize:

• Diagonal of the second square is 8 cm, which is option A.

This shortcut works for any square whose area gets doubled, so it is worth remembering.