Question

The diagonal of a square $2\sqrt{2}$ cm.Find the length of the sides of the square

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

Answer 1

The correct option is B

2 cm

Angles of $\Delta ABC$ are ${45}^{\circ },{45}^{\circ },{90}^{\circ }$

$\Rightarrow \sin \left(45\right):\sin \left(45\right):\sin \left(90\right)$

$\Rightarrow \frac{1}{\sqrt{2}}:\frac{1}{\sqrt{2}}:1$

$\Rightarrow 1:1:\sqrt{2}$

The ratio of side AB,BC,AC will be in the ratio $1:1:\sqrt{2}$

Let the side AB,BC,AC be $x,x,\sqrt{2}x$

So, $\sqrt{2}x=2\sqrt{2}\Rightarrow x=2cm$

Hence AB = BC =2 cm