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Nikhil Manohar

· started a discussion

· 1 Months ago

ans (Question: 351236.0 )

option A

Question:

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

Options:
A)

22+1    

B)

22-1    

C)

22+1    

D)

22-1    

Solution:

Ans: (c)


Knowledge Expert

· commented

· 1 Months ago

Dear Student,

Let consider,
ABCD is square and PQRSTUVW is octagon with equal sides constructed with in the square.
In order to have octagon with equal sides, we should have AP=QB=BR=SC=CT=….
Let AP=AW=x; (all sides which cut)
Let PQ = y; as all sides of octagon are equal, QR=RS=ST=TU=UV=VW=WP=y;
As the length of side of square is 2,
2x+y = 2 ------(1)
Applying Pythagoras to the right triangle APW, y2 = x2+x2 = 2x2
=> y= x√2 ------(2)
Solving (1) and (2):
2x+x√2 = 2 => x = 2/(2+√2) = √2/(√2+1)
=> y = x√2 = 2/(√2+1)

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