Question

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

• A. $8cm$
• B. $8\sqrt{2}cm$
• C. $16cm$
• D. $4\sqrt{2}cm$

Answer 1

The correct option is A $8cm$

Area of square with diagonal $4\sqrt{2}$ cm
$=\frac{1}{2}\times \left(diagonal\right)=\frac{1}{2}\times {\left(4\sqrt{2}\right)}^{2}c{m}^2=16c{m}^2$
Area of the second square $=2\times 16c{m}^2=32c{m}^2$

Let $d$ cm be diagonal of the second square. Then,
$\frac{1}{2}{d}^2=32c{m}^2$

$\Rightarrow d^2=2\times 32c{m}^2$
$\Rightarrow d=\sqrt{64}=8cm$