A square whose side is 2m 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 meters is 

Dear Student,

We have a square ABCD  , And AB =  BC  =  CD  =  DA =  2  m

And we form a regular octagon by cutting all four corner . 

Let  EF  =  FG =  GH  =  HI  =  IJ  =  JK  =  KL =  LE  =  x

And as we form a regular octagon , So by symmetry we get

AE  =  AL  = BG  =  BF  =  CH  =  CI  =  DJ  =  DK  =  a 

Now we apply Pythagoras theorem in triangle ALE  , and get

AL²  +  AE²  =  LE²

By substituting all values , we get

a² +  a²   =  x²

x²  =  2a²

a²  =

a  =                                                                  --------------- ( 1 )

And

AB  =  AE +  EF  +  FB 

2  = a + x  + a

2a + x   =  2    , Now we substitute value from equation 1 , we get 

$$\begin{gathered} 2\left(\frac{\mathrm{x}}{\sqrt{2}}\right)+\mathrm{x} = 2 , \mathrm{now} \mathrm{we} \mathrm{simplify} \mathrm{it} \mathrm{as}: \\ \sqrt{2}\times \sqrt{2}\times \frac{\mathrm{x}}{\sqrt{2}}+\mathrm{x} = 2 \\ \sqrt{2}\mathrm{x}+\mathrm{x} = 2 \\ \mathrm{x}\left(\sqrt{2}+1\right) = 2 \\ \mathrm{x} = \frac{2}{\sqrt{2}+1} \\ \mathrm{So}, \mathrm{sides} \mathrm{of} \mathrm{octagon} = \frac{2}{\sqrt{2}+1} \mathrm{m} \end{gathered}$$ 

Regards