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A square, whose side is $2$ metres, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres is

  1. $\frac{\sqrt{2}}{\sqrt{2}+1}$
  2. $\frac{2}{\sqrt{2}+1}$
  3. $\frac{2}{\sqrt{2} - 1}$
  4. $\frac{\sqrt{2}}{\sqrt{2}-1}$
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Option 2 is correct

X+2y=2.............(i) metre (square side)

X^2=y^2+y^2

Y=x/ sqrt(2)....... (ii)

Frm both eqns

X(sqrt(2) +1)=2

X=2/(sqrt(2) +1)

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