A carom board (40 cm × 40 cm) has the queen at the centre. When the queen is hit by the striker, it moves to the front edge, rebounds and goes into the hole behind the striking line. The displacement of the queen is 

Given that

A carom board has dimensions $\left(40\text{cm}\times 40\text{cm}\right)$

S = 40cm

Queen is at center i.e YC = 20cm

When it is hit by striker

It moves to front edge X and goes in to the hole at A as shown.

The displacement of queen = AC

From right angle triangle we get ${\text{AC}}^{\text{2}}={\text{CY}}^{\text{2}}+{\text{YA}}^{\text{2}}$

${\text{AC}}^{\text{2}}=400+400$

$\text{AC}=\sqrt{800}$

$=\sqrt{400\times 2}=\sqrt{{\left(20\right)}^2\times 2}$

$\text{AC}=20\sqrt{2}$