Question

a square, whose side is 4 metre has its corner cut away so as to form an octagon with all sides equal .find the length of each side of the octagon.

Please please answer right

And In The Root Form

Answer 1

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Answer 2

• Let side of square be M.

• And x be the length of square.

In $\triangle$ALE

By Pythagoras Theorem

=> LE² = AL² + AE²

=> x² = a² +  a² 

=> x²  =  2a²

=> x²/2 = a²

=> a = $\sqrt{ {x}^{2} /2}$ _______ (eq 1)

Now.. we can write AB as

=> AB  =  AE +  EF  +  FB 

=> 4 = a + x  + a

=> 4 = 2a + x

=> 4 = 2( $\sqrt{ {x}^{2} /2}$) + x

=> 4 = $\sqrt{2}$ x + x

=> 4 = x($\sqrt{2}$ + 1)

=> 4/($\sqrt{2}$ + 1) = x

On rationalization we get,

=> x = 4($\sqrt{2}$ - 1)

=> x = 4(1.41 - 1)

=> x = 4(0.41)

=> x = 1.64 m

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