Question

The length of a side of a square is 3 cm. Length of its diagonal will be equal to

• A. 6 cm
• B. $3\sqrt{2}$ cm
• C. $6\sqrt{2}$ cm
• D. 3 cm

Answer 1

The correct option is B

$3\sqrt{2}$ cm

Here, angles of $△ABC$ are ${45}^{\circ },{45}^{\circ },{90}^{\circ }$

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

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

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

So, the sides AB,BC & AC will be in the ratio of $1:1:\sqrt{2}$

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

$\Rightarrow x=AB=3$

$\Rightarrow AC=x\sqrt{2}=3\sqrt{2}$ cm