CAT 2001 — QA Question 2

Let the side of the octagon be x, which is also the hypotenuse of the triangle in the corner of the square.

∴ TYhe other two sides of the triangle = $\frac{x}{\sqrt{2}}$

$\frac{x}{\sqrt{2}}+x+\frac{x}{\sqrt{2}}=2$

$x=\frac{2}{\sqrt{2}+1}$

Hence, option (b).