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1. 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

Solution:

\begin{aligned} d = 4 \sqrt{2} c m \\ \Rightarrow Area = \frac{1}{2} d_{1}^{2} \\ = \frac{1}{2} \times {(4 \sqrt{2})}^{2} \\ =  16 c m^{2} \end{aligned}

Area of new square = (2 × 16) cm² = 32 cm²

\begin{aligned} ∴ \frac{1}{2} d_{2}^{2} = 32 \\ \Rightarrow d_{2}^{2} = 64 \\ \Rightarrow d_{2} = 8 c m \end{aligned}

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